Scribd
Upload
118 views2 pages

Vector 1

This document contains 22 practice questions on vectors for students. The questions cover a range of topics including: finding unit vectors; determining if points are collinear; finding vectors parallel or perpendicular to other vectors; using vectors to find areas of triangles; and vector identities involving magnitudes, sums, and cross products. The answers to selected questions are provided.

Uploaded by

Shaquib khan
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
118 views2 pages

Vector 1

This document contains 22 practice questions on vectors for students. The questions cover a range of topics including: finding unit vectors; determining if points are collinear; finding vectors parallel or perpendicular to other vectors; using vectors to find areas of triangles; and vector identities involving magnitudes, sums, and cross products. The answers to selected questions are provided.

Uploaded by

Shaquib khan
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
You are on page 1/ 2

Chapter Practicce

2 Marks Questions

1. Write a unit vector in the direction of the sum of vectors a =2i 2i+2j-5h and
b =2i +j-7k.
2. If a = 4i -j +k and b =2i -2j+X, then find a unit vector parallel to vector a+
3. If PO +0Q = Q0 +OR, then show that points P, Q and R are collinear.

4. Ifa 2i +2j+3h, b=-î+2+hand e 8i + jaresuchthat a +i


= =
bis perpendieularlar
to c then find the vlaue of A.

3 Marks Questions

5. Let a =i +j +h,b 4i -2 +3Xand c =i


= -

2j+k andfind avector ofmagnitude6


units which is parallel to the vector 2 a - b +3 c.

6: A vector r is inclined at equal angles to the three axes. Ifthe magnitude of r is


23 units, then find the value of r.

7. Ifa unit vector a makes anglewith i, with j and an acute angle6 with k, thenfind
3
the components of a and the angle 6.
8. Find the position vector of a point C which divides the line segment joining A and B
whose position vectors are 2 a+ b and a -3 6,externally in the ratio 1:2. Also, show
that A is the mid-point of the line segment BC.
9. Points L, M and N divide the sides BC, CA and AB of AABC in the ratio 1:4, 3:2 and

3:7, respectively. Prove that AL+BM+ CN is a vector parallel to CK, where k divides
AB in the ratio 1:3.

10. 1f a =2+i-3k and b=i-2j +h then find a vector of magnitude 5 units


perpendicular to both a and b.
11. Ifa =i +j+hand b =j -k, thenfind avector c,suchthat ax c =banda c=3
12. Using vectors, find the area oftriangle with vertices A(1,1,2), B(2,3,5) and C(1,5.5).
ectors

13. If a,b and c are three vectors, such that |al= 5,|bl=12 cl= 13 and a+ b+ c =0 then
find the value of a-b+b.c+c-a.
vectors
by the
14. The diagonals AC and BD of a parallelogram ABCD are represented
i+j-kand i - j +k, respectively. Find the area of the parallelogram.
4 Marks Questions
OX, OY and OZ.
15. Show that the vector i +j +k is equally inclined at axes

from right
=3i -2)+h, b =i-3j+5X andc =2j+j-4k
a
16. Show that the vectors a
angled triangle.
17. Prove that for any two vectors a and b, 1lal +bl slal +| 61
a +b c =0. Then prove that
18. If a, b and c are three vectors such that +

axb b xc = cxa.

5 Marks Questions
a. Prove that a, b and care
a, b and c are three vectorssuchthat ax6= c, bxc
=

19.

mutually at right angle and lbl 1,Iel la


= =

each other, then prove that


20. If a, b and c are perpendicular to
(a 6 x c = a'b'e.
to the opposite sides are
21. Prove that the perpendiculars from the vertices of a triangle
concurrent.
. b +- a2
22. In any AABC, prove by vector method, cos A=
2bc

Answers
26-3+2k 4. A=8

5. 21-4+ 4k 6.+2 +j+) 7. -and component of a =


10.+j+ k)
8. Position vector of c -33+56 3

12 13. -169 14. V2 sq units

You might also like