Iducatton

NAVEEN SHARMA 9811628340, 9811528340

THINK PHYSICS BY NAVEEN SHARMA
VECTORS (Objective)
Class - XI(2025 -26)
1. If the resultant of two forces of magnitudes P and Q acting at
apoint at an angle o
is 7Q. then P/Q is
(a) | (b)3/2 (c) 2 (d) 4
2. The resultant of two forces F and F; is P. IfF, is reversed, then resultant is Q. Then the
value of (P+)in terms ofF and F; is
(a) 2(F +E;) (b) E+ (c) (FË+F? (d) None of these
3
Aman moves towards 3m north then 4m towards east and finally Sm towards 37° south
of west. His displacement from origin is
(a) 5/2m (b) Om (c) Im (d) 12m
4. Three forces P, Q &R are acting at a point in the plane. The angle between P & Qand
Q & R are 150° & 120° respectively, then for equilibrium, forces P, Q & R are in the
ratio
(a) 1:2:3 (b) 1:2:N3 (c) 3:2:1 (d) /3 :2:1
5. Aman rows a boat with a speed of 18 km/hr in northwest direction. The shoreline makes
an angle of 15° south of west. Obtain the component of the velocity of the boat along
the shoreline.
(a) 9 km/hr (b) 18Ykm I hr (C) 18 cos 15° km/hr (d) 18 cos 75° km/hr
2
6. A bird moves from point (1, -2, 3) to (4, 2, 3). If the speed of the bird is 1Om/sec, then
the velocity vector of the bird is
a) s(f-2j+ 3É) (b) s(4i+2j+36) (c) 0.6i +08) (d) 6i +8,
7. The resultant of two forces, one double the other in magnitude is perpendicular to the
smaller of the two forces. The angle between the two forces is
(a) 150° (b) 90 (c) 60° (d) 120º
8. If the angle between the unit vectors a and band is 60°, then a-b is
(a) 0 (b) 1 (c) 2 (d) 4
9. Two forces each numerically equal to 10 dynes are acting as shown in the following
figure, then their resultant is
10 dynes

S60° 10 dynes
(a) 10 dynes (b) 20 dynes (c) 10/3 dynes
(d) 5 dynes
10. Two vectors Aand B and are such that |j+BÄ-B. The angle between the vectors
Aand B is -
(a) 0 (b) /3 (c) r/2 (d) n
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 Education NAVEEN SHARMA 9811628340, 9811528340
11. Aparticle moves through angular displacement 9 on a circular path of radius r. The
linear displacement will be -
(a) 2r sin (0/2) (b) 2r cos (0/2) (c) 2r tan (0/2) (d) 2r cot (0/2)

12. The vector Pmakes 120° with the x-axis and vector omakes 30° with the y-axis. What
is their resultant?
(a) P+ Q (b) P-Q (c) Jp' +g' (d) p
13. A man travels I mile due east, then 5 miles due south, then 2 miles due east and finally
9 miles due north, how far is he from the starting point -
(a) 3 miles (b) 5 miles (c) 4 miles (d) between 5 and9 miles
14. The angle that the vector A= 2i +3 makes with y-axis is
(a) tan (3/2) (b) tan' (2/3) (c) sin(2/3) (d) cos"(3/2)
15. Aman moves towards 3m north then 4m towards east and finally 5 m towards 37° south
of west. His displacement from origin is -
(a) 5V2m (b) Om (c) 12 m (d) 5 m
16. If 3i +2j+ 8k and 2i+xË+kare at right angles that x =
(a) 7 (b) -7 (c) 5 (d)4
17. a,i + a,j is a unit vector perpendicular to 4? -3jif -
(a) a, =.6, a) =.8 (b) aj =3, a, =4 (c) aj =.8, a =.6 (d) aj =4, a) -3
18. If ais a vector and x is a non-zero scalar,
then -
(a) xa is a vector in the direction of
(b) xa is a vector collinear to
(c) xaand have independent directions (d) None of these
SUBJECTIVE TYPE PROBLEMS
19. Two vectors have magnitudes 3 unit and 4 unit respectively.
between them if What should be the angle
the magnitude of the resultant is
(a) lunit (b) 5 unit and (c) 7 unit
20. When two forces of magnitude P and Q are perpendicular to each other, their
resultant
is of magnitude R. When they are at an angle of 180° to each other their resultant
is of
magnitude R, Find the ratio of P and Q.
V2
21. A body acted upon by 3given forces is under equilibrium.
y4
F,

e 37

(a) If F=10NI F:=6NI, Find the values of F,|&angle (0)

(b) Express F,in unit vector form
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(HR)
 Iducaton
22. NAVEEN SHARMA 981 1628340,9811528340
I1 the four forces as shown arc in cquilibrium Express
F&7in unit vector form
15 N

,10 N

37V30°

23. A particle forces

IS acted upon by the
Fi=2i +j-34,F: =Si +j- bi. Fi =bi +5j-7X. F, =ci +6j-ak Find the values of
the constants a, b, c in order that the particle will be in equilibrium.
24.
Aplane body has perpendicular axes OX and OY marked on it and is acted on by
following forces
SP in the direction OY
4P in the direction OX
10P in the direction OA where A is the point (3a, 4a)
15P in the direction ABwhere B is the point (-a, a)
Express each force in the unit vector from &calculate the magnitude &direction of sum
of the vector of these forces.
25. Avector Aof length 10 units makes an angle of 60° with the vector Bof length 6 units.
Find the magnitude of the vector difference 4-B &he angle it mkes with vector Å.
26. (a) Calculate r =a-b+c where a=5i +4j-6k, b =-2í +2j-3k and c= 4i +3)+2k.
(b) Calculate the angle between r and the z axis.
(c) Find the angle between a and b.
27. The volume of the parallelepiped whose sides are given by
04 =2i-2j, OB =i+j-k, 0C =3i-k is
(a) 4 (b) 2 (c) 2 (d) None of these
13 7
28. Thepoints with position vectors 60i+3j,40i8j.ai - 52jare collinear of
(a) a= -40 (b) a = 40 (c) a=20 (d) None of these
29. If A, B.are three non coplanar vector, then (7 +8+c)(Ä+B)(+c)|equals
(a) 0 (b) ABC (e) 2AB| (d) - ABC |
30. Let a =2i+j-2k and b=itj. Ifc is avector such that ac=ldi-d -2V2 and the angle
between (axó) and cis 30°, then
(a) 2/3 (b) 3/2 (c) 2 (d) 3

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 Luaton
NAVEEN SHARMA 9811628340, 9811528340
31. Ifa and b are two unit vectos such that a +2h and Sa- 4h
are perpendicular to
cach other than the angle between a and b is
(a) 45° 2
(b)60° (c) cos (d) cos
7

Objective Type Problems ANSWERKEY

1. (c) 2. (a) 3. (b) 4. (d) S. (a) 6. (d) 7. (d)
8. (b) 9. (a) 10. (c) 11. (a) 12. (a) 13. (b) 14. (b)
15. (b) 16. (b) 17. (a) 18. (b)

Subjective Type Problems

19. (a) 180°, (b) 90°, (c) 0

20. 2tV3 21. (a) |F=8N,0 =90° (b) F2 =6i

22.
F;--(|2/5-1)jeF: -(2-s/i)i-(2/5 -1s)i
23. a=-7, b=-3, c= -4
24.
SPj,4Pi,6Pi +8Pj, -12Pi -9Pj, V20P,tan" [-2]with +ve xaxis.
25.
2V19;cos
2V19
26. (a) 1i+5, -7X, (b) Cos- 7
cos -20
V1309
27. (b) 28. (a) 29. (d) 30. (b) 31. (b)

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 Iducation
NAVEEN SHARMA 9811628340, 9811528340
THINK PHYSICSBY NAVEEN SHARMA
Class - I(2025 - 26)
Vectors (Subjective)
1.
Aparticle has a displacement of 12m towards east and Sm towards the north ad then
vertically upwards. Find the magnitude of the sum of these displacements. 6m
2. Two vectors, both equal in magnitude, have their resultant equal in magnitude of the
either. Find the angle between the two vectors.
3.
Iwo forces whose magnitude are in the ratio of 3:5 give a resultant of 35N. If the angle
of inclination be 60°, calculate the magnitude of cach force.
4. Twoforces P and 2P newton act on aparticle. If the first be doubled and the second be
increased by 20 Newton, the direction of the resultant is unaltered. Find the value ofP.
5.
The greatestand the least resultant of two forces acting at a point are 29N and 5N
respectively. Ifeach force is increased by 3N, find the resultant of two new forces acting
at right angle to cach other.
6. The sum of the magnitude of two forces acting at a point is 18N and the magnitude of
their resultant is 12N. If the resultant makes an angle of 90 with the force of smaller
magnitude, what are the magnitude of the two forces?
7. Four forces P,2P,3P and 4Pact along sides of a square taken in order. Find their
resultant.

8. In a regular hexagon ABCDEF prove that AB +AC+AD+ AE+AF =640.

9.
If a+b+e=o and la =V37,(6)=3,-4then find the angle between band c.
10. Aparallelogram is constructed on 5a+2b and a-3b. Given that a =2/2.B= 3and
angle between a &b is 4I.Then find length of the longer diagonal.
11. A car travels ókm towards north at an angle of 45° to the east and then travels distance
of 4km toward north at an angle of 135° to the east. Howfar is the point from the starting
point? What angle does the straight line joining its initial and final position makes with
the east? N

4 km
6 km
459
W+ E(X)

S(n

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 1heaion
NAVEEN SHARMA 9811628340, 9811528340
12. There arc two force vectors, onc of SN and other of 12N At what angle should the tw.
vCctors be added to get the resultant vector |7N, 7N, and 13N respcctively?
13. GIven that 4+ B+C=0. Out of three vectors, the two are equal in magnitude and the
magnitude of third vector is v2 times that either of the two having cqual magnitude
Then findangles between vectors.

14. If A=4i-3j and B=6i+8 ji. then find the magnitude and
direction of A+ B.
15. A truck travelling due north at 20ms' turns west and travels at
the same speed. Find the
change in its velocity.
16. If the sum of two unit vectors is a unit vector, then find the
magnitude of difference.
17. The sum of the magnitudes of two forces acting at a point is 18 and
their resultant is 12. If the resultant is at 90° with the force the magnitude of
of smaller magnitude, what
are the magnitudes of forces?
18. Two forces FË = IN and F =2N act along the lines x = 0 and y= 0,
find the resultant of forces. respectively. Then
19. Let A=2i+j, B=3j-k and C=6i-2k. Find the value of A=-2B+ 2C.
20. A vector ais turned without a change in its length through a small angle d. Find the
value of Aa and Aa.
21. An object of m kg with speed of v ms strikes a wall at an angle and rebounds at the
same speed and same angle. Find the magnitude of change in the momentum of object.

22.. If A-3i+4j and B=7i+24), find the vector having the same magnitude as Band
parallel to A.
23. Vector Ämakes equal angle withx-, y-, and z-axis. Find the value ofits components (in
terms of magnitude ofå ).
24. Find the vector that must be added to the vector i-3 j+2k and 3 j+6k-7k so that the
resultant vector is aunit vector along the y-axis.
25. Atwhat angle should the two force vectors 2F and V2 Fact so that the resultant force
is VIOF?
26. Two forces, while acting on a particle in opposite directions, have the resultant of 10N.
If they act at right angles to each other, the resultant is found to be 50N. Find the two
forces.

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 Iducalion
27. Two forcCs cach cqual to F/2 act NAVEEN SHARMA 9811628340, 9811528340
at
third force acting along their biscctor right angle Their cffcct may
of that third force? in the opposite direction. Whathc isncutral1zed by a
the
magnitude
28. The resultant of two forces has
magnitude 20N. One of the forces is of
20/3N and makes an angle of 30° magnitude
the other fore? with the resultant. Then what is the magnitude of
29. The resultant of Pand ) is R.If o is doubled, X
is doubled, when Q is reversed, R is
again doubled, find P:Q:R.
30. A=2i+4 j+4k and B= 4i+ 2 j-4k are two vectors.
Find the angle between them.
32. If two vectors 2i+3 j-k and -4j-6j-dk are parallel to
of .
each other, then find the value
32. InQ. 21, if vectors are perpendicular to each other then find
the value of .
33. If A=2i+3 j-k and B=-i+3 j+4k,then find the
projection of Aon B.
34. A body, acted upon by a force of 50N, is displaced through a distance 10m in a
making an angle of 60° with the force. Find the work done by the force. direction
35. A particle move from position 3i+2j-6k to 14i+13 j+9k due to a uniform force of
4i+ j+3k N. Ifthe displacement is in meters, then find the work
done.
36. If for two vectors Aand B, sum +B) is perpendicular to the difference(4-B).
Find
the ratio of their magnitude.
37. A force F=-K yi+xj (where Kis apositive constant) acts on a particle moving in
the x-y plane. Starting from the origin, the particle is taken along the positive
x-axis to
the point (a, 0) and then parallel to the y-axis to the point (a, a). Find the total
done by the forces Fon the particle. work

38. If A=3i+ j+2k and B= 2i-2j+4k, then find the value of 4x B.

39. The vectors from origin to the points A and B are A=3i-6j+ 2k and B= 2i+ j-2k
respectively. Find the area of the triangle OAB.
40. The angle between the vectors Áand Bis 0. Find the value of the triple
product

41. Find the torque of the force F:

F-(i-3j-41 Nacting at the point r= 3i+2j+3k m

about the origin.

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 Lducaton
NAVEEN SHARMA 9811628340, 9811528340
42. If aparticle of mass m is moving with constant
velocity
parallclto x-axis in xv planc as shown in figure. Find its angularv
momentumwith respect to origin at any timet.

ANSWER KEY
1. (14.32m) 2. (0 =120°)
3. (25 N) 4. (10 N)
(25 N) 6. (5 N, 13 N)
7.
(2N2P,225° with x-axis) 9. (60°)
10. (V593) 11. 9=tan (5)
12. For 17N, both the vectors, should be parallel, i.e.,
For 7N,both the vectors should be antiparallel, i.e. angle between them should be zero.
For 13N, both the vectors should be angle between them should be 180°.
them should be 90°. perpendicular to each other, i.e., angle between
13. Angle between Aand B, a =90°, Angle between Band C,
and C, y 135° B= 135°, Angle between A

14. 4+B-s/5, =tan

15. Av= 2042 and direction tan(1)45°, i.e., S - W

16. 3 17. P=5 andQ= 13 18. F=2i+j
19. 20i-5 j-4k 20. Ad=ade, Aq= 0 21. 2mvcos
22. 15i+ 20 j 23. A, =4, = 4, =Acosa = A
V3
24. -4i-2 j+ 5k 25. =45° 26. A
= 40N and B= 30N
27. FIV2 28. 20N 29. VR and P=R
30. 9=90° 31. =2 32. 2=-26
33. The projection of ~on B= 34.
V26 250J
35. 100 J 36. A/B = 1
37. Total work done = -Ka'
38. x-&/5
39. 5Vi7 A

Area of AOAB = sq. unit 40. 41. 17i-6j-13k

2

42. L=-mvbk

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