Three Dimensional Geometry Test-1 Notes - Class 12

Class 12: Three Dimensional Geometry Test-1 Notes - Class 12

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CBSE TEST PAPER-06 
CLASS - XII MATHEMATICS (Vectors & Three Dimensional Geometry) 
Topic: - Three Dimensional Geometry 
1. Find the directions cosines of x, y and z axis. [1] 
2. Find the vector equation for the line passing through the points (-1,0,2) and
(3,4,6)
[1]  
3. Find the angle between the vector having direction ratios 3,4,5 and 4, -3, 5.
[1] 
4. 
Find the vector and Cartesian equation of the line through the point (5, 2,-4)
and which is parallel to the vector  
? ?
3 2 8 i j k + - ?
[4] 
5. 
Find the angle between the lines
? ? ? 
? ? ? ?
(3 2 ) ( 2 )
(2 56 ) (3 5 4 )
r i j k i j k
r i j k i j k
?
µ
= + - + - - = - - + - - 
? ?

? ?
[4] 
6. 
Find the shortest distance between the lines
? ? ? ?
? ? ?
( 2 ) ( )
(2 ) (2 2 )
r i j k i j k
r i j k i j k
?
µ
= + + + - +
= - - + + +

? ?
 
? ?
[4] 
7. Find the direction cosines of the unit vector ? to the plane
? ?
.(6 3 2 ) 1 0 r i j k - - + =

?
passing through the origin.
[4] 
8. Find the angle between the two planes 3x – 6y + 2z = 7 and 2x + 2y - 2z = 5
[4] 
9. 
Find the vector equation of the plane passing through the intersection of
planes 
? ? ? ?
.( ) 6    .(2 3 4 ) 5 r i j k and r i j k + + = + + = -  
? ?
And the point (1,1,1)
[6] 
10. Find the coordinate where the line thorough (3,-4,-5) and ((2,-3,1) crosses
the plane 2x + y + z = 7
[6] 
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