Page 1 CBSE TEST PAPER08 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 xy + 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]Read More
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