Page 1 CBSE TEST PAPER06 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]Read More
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