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# Three Dimensional Geometry Test-2 Class 12 Notes | EduRev

## Class 12 : Three Dimensional Geometry Test-2 Class 12 Notes | EduRev

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CBSE TEST PAPER-07
CLASS - XII MATHEMATICS (Vectors & Three Dimensional Geometry)
Topic: - Three Dimensional Geometry
1. What is the direction ratios of the line segment joining  P(x 1 y 1 z 1) and Q (x 2
y 2 z 2)

2.
The Cartesian equation of a line is
3 5 6
2 4 2
x y z + - +
= = Find the vector
equation for the line.

3.
Show that the lines
3 1 5 1 2 5
3 1 5 1 2 5
x y z x y z
and
+ - - + - - = = = =
- - are
coplanar.

4.
Find the shortest between the l 1 and l 2 whose vectors equations are
? ? ?
? ? ? ?
(2 )
2 (3 5 2 )
r i j i j k
r i j k i j k
?
µ
= + + - +
= + - + - +

? ?

? ?

5.
Find the angel between lines
? ? ? ?
? ? ?
(2 5 ) (3 2 6 )
(7 6 ) ( 2 2 )
r i j k i j k
r i k i j k
?
µ
= - + + + +
= - + +

? ?

? ?

6.
Show that the lines
5 2
7 5 1 1 2 3
x y z x y z
and
- +
= = = =
- Are perpendicular to each
others

7.
Find the vector equations of the plane passing through the points R(2,5,-3),
Q(-2,-3,5) and T (5,3,-3)

8.
Find the Cartesian equation of the plane
? ?
.( ) 2 r i j k + - =

?

9. Find the equation of the plane through the intersection of the planes
3x – y + 2z -4 = 0 and x + y + z – 2 = 0 and the point (2,2,1)

10.
If the points (1,1p) and (-3,0,1)be equidistant from the plane
? ?
.(3 4 12 ) 13 0 r i j k + - + =

?
, then find the value of p.

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