Three Dimensional Geometry Test-2 Class 12 Notes | EduRev

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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)
[1] 
2. 
The Cartesian equation of a line is 
3 5 6
2 4 2
x y z + - +
= = Find the vector 
equation for the line. 
[1]  
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. 
[1] 
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
= + + - +
= + - + - +

? ?

? ?
[4] 
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
= - + + + +
= - + +

? ?

? ?
[4] 
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 
[4] 
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) 
[4] 
8.
Find the Cartesian equation of the plane 
? ?
.( ) 2 r i j k + - =

?
[4] 
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) 
[6] 
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.
[6] 
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