Page 1 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]Read More

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