3-D Geometry
I.ASSERTION AND REASON QUESTIONS
Study the two statements labelled as assertion ( A ) reason ( R ) . Point out if :
( A ) Both Assertion and reason are true and reason is the correct explanation of assertion .
( B ) Assertion and reason both are true but reason is not the correct explanation of
assertion .
( C ) Assertion is true , reason is false .
( D ) Assertion is false , reason is true .
1.Assertion : The Perpendicular distance from point (2,1,-1) from the plane x - 2y + 4z = 9
is
Reason : The Perpendicular distance p from point P ( x1 , y1,21 ) to the plane Ax + By + Cz
+ D = 0 is given by
p = modulus of Ax1+By1+Cz1 -D
( A2 + B2 + C2 )½
2. Assertion : Equation of plane cuts intercepts 2,3 and 4 on the x - axis , y - axis and z -
axis respectively then its equation is 6x + 4y + 3z = 1.
Reason : If Plane cuts intercepts a , b and c on the x - axis , y - axis and z - axis respectively
then its equation is x +y +z =1.
a b c
3. Assertion : Lines X-1 = y-3 = Z-3 and x-4 = y-1 = z are skew line.
2 3 4 5 2
Reason : Two lines are called Skew iff they are neither parallel nor intersecting +2 -1 -2 - 3
+1
4. Assertion : lines x+2 = y-1 = z-2 and x-3 = y = z+1 are coplanar.
-2 3 1 -3 -2 2
Reason : if two lines are perpendicular then these lines are coplanar .
5. Assertion : Direction cosine of the normal to the plane 2x - 3y - 6z - 3=0 are (2/7,-3/7,-
6/7).
Reason : direction cosines are equal to the direction ratios.
6. Assertion : The direction cosine of a line are cosa , cosẞ and
cosy where a ẞ and y are the angles made by the line with x , y
and z - axis respectively ;
Reason : If a line makes angles 90 ° , 135 ° , 45 ° with x , y and z - axes respectively , then
it's direction cosines are (0, -1 , 1 ).
2½ 2½
7. Assertion : The points ( 2,3,4 ) , ( -1 , -2,1 ) and ( 5,8,7 ) are collinear .
Reason : The direction ratios of line segment joining two points P ( x1 , y1,21 ) and Q ( x2
y2,Z2 ) are ( X1 - X2 ) , ( y1- y2 ) and ( Z1 - Z2).
8. Assertion : equations of the plane passing through the points R ( 2 , 5 , -3 ) , S (-2 , -3 , 5)
1
and T ( 5 , 3 , -3 ) can be given by ax + by + cz + d = 0 , where a , b , c are the dc's of the
normal to the plane
Reason : there can be passed infinitely many points from three non - collinear points.
9. Assertion ( A ) : 3x + 2y - z = 7 and 6x + 4y- 2z = 3 are parallel planes .
Reason ( R ) : Direction ratio of normal of two parallel planes are proportional .
10.Assertion ( A ) : Distance between 3x + 2y - z = 7 and 6x + 4y - 2z = 3 is 4 unit.
Reason ( R ) : Distance between two parallel planes can be given by
II.LONG ANSWER TYPE QUESTIONS
1.Find the image point(1,2,1) w.r.to the line x-3 = y+1 = z-1
1 2 3
also find the equation of the line joining the given point and its image.
2. line passes through the point with position vector 2î – ĵ + 4k̂ and is in the direction of.
the vector î + ĵ – 2k̂. Find the equation of the line in cartesian form.
3. Find the distance between the planes 2x + 2y – z + 2 = 0 and 4x + 4y – 2z + 5 = 0.
4.Two points (-2,4,-5)and (1,2,3)are located on a certain line. Find the direction cosines of
the line passing through these points.
5. Find the shortest distance between the two lines given below.
x-83=y+9-16=z-107 and x-153=y-298=z-55
Thank You
Guided by: Done by :
U.Jayaprakash(sir) T.Rakshith k umar
( P.G.T)Maths XII th (1031)
