Three Dimensional Geometry Test-3 - Class 12

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CBSE TEST PAPER-08 
CLASS - XII MATHEMATICS (Vectors & Three Dimensional Geometry) 
Topic: - Three Dimensional Geometry 
1. If a line has the direction ratios -18, 12, -4 then what are its   direction cosines [1] 
2. 
Find the angle between the pair of line given by
? ? ? ?
( )
? ? ?
3 2 4 2 2
5 2 (3 2 6 )
r i j k i j k
r i j i j k
?
µ
= + - + + +
= - + + +

? ?

? ?
[1]  
3. Prove that the points A(2,1,3) B(5, 0,5)and C(-4, 3,-1) are collinear
[1] 
4. 
find the distance between the lines l
1 
and l
2
 given by
? ? ? ?
? ? ? ?
2 4 (2 3 6 )
3 3 5 (2 3 6 )
r i j k i j k
r i j k i j k
?
µ
= + - + + +
= + - + + +

? ?

? ?
[4] 
5. 
Find the angle between lines
5 2 3
,
2 2 1 4 1 8
x y z x y z - - - = = = =
[4] 
6. 
Find the shortest distance between the lines 
1 1 1 3 5 7
7 6 1 1 2 1
x y z x y z
and
+ + + - - - = = = =
- - [4] 
7. 
Find the vector and Cartesian equations of the plane which passes through the 
point (5,2,-4) and ? to the line with direction ratios (2,3,-1)
[4] 
8. 
Find the Cartesian equation of the plane 
? ?
[(5 2 ) (3 ) (25 ) ] 15 r t i t j t k - + - + + =

?
[4] 
9. 
Find the equation of the plane through the line of intersection of the planes 
x +y +z = 1 and 2x + 3y + 4z = 5 which is ? of the plane x-y + z = 0
[6] 
10. 
Find the distance of the point (-1,-5,-10) from the point of intersection of the line 
? ? ? ?
(2 2 ) (3 4 2 ) r i j k i j k ? = - + + + +

? ?
and the plane  
? ?
.( ) 5 r i j k - + =

?
[6]