Page 1 CBSE TEST PAPER-07 CLASS - XII MATHEMATICS (Vectors & Three Dimensional Geometry) Topic: - Three Dimensional Geometry 1. What is the direction ratios of the line segment joining P(x 1 y 1 z 1) and Q (x 2 y 2 z 2) [1] 2. The Cartesian equation of a line is 3 5 6 2 4 2 x y z + - + = = Find the vector equation for the line. [1] 3. Show that the lines 3 1 5 1 2 5 3 1 5 1 2 5 x y z x y z and + - - + - - = = = = - - are coplanar. [1] 4. Find the shortest between the l 1 and l 2 whose vectors equations are ? ? ? ? ? ? ? (2 ) 2 (3 5 2 ) r i j i j k r i j k i j k ? µ = + + - + = + - + - + ? ? ? ? [4] 5. Find the angel between lines ? ? ? ? ? ? ? (2 5 ) (3 2 6 ) (7 6 ) ( 2 2 ) r i j k i j k r i k i j k ? µ = - + + + + = - + + ? ? ? ? [4] 6. Show that the lines 5 2 7 5 1 1 2 3 x y z x y z and - + = = = = - Are perpendicular to each others [4] 7. Find the vector equations of the plane passing through the points R(2,5,-3), Q(-2,-3,5) and T (5,3,-3) [4] 8. Find the Cartesian equation of the plane ? ? .( ) 2 r i j k + - = ? [4] 9. Find the equation of the plane through the intersection of the planes 3x – y + 2z -4 = 0 and x + y + z – 2 = 0 and the point (2,2,1) [6] 10. If the points (1,1p) and (-3,0,1)be equidistant from the plane ? ? .(3 4 12 ) 13 0 r i j k + - + = ? , then find the value of p. [6]Read More

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