Page 1 CBSE TEST PAPER-05 CLASS - XII MATHEMATICS (Vectors & Three Dimensional Geometry) Topic: - Vectors 1. Is the measure of 1000 cm 3 is scalar or vector. [1] 2. Write two different vectors having same direction. [1] 3. Find the direction ratios and the direction cosines of the vector ? ? 2 r i j k = + - ? [1] 4. Find angle between two vectors 1, 2 . 1 a and b if a b a b = = = [1] 5. Find a vector in the direction of vector ? 2 a i j = - ? that has magnitude 7 units. [1] 6. If ? ? a i j k = + + ? , ? ? b j k = - find a vector c such that . . 3 a c b and a c × = = [4] 7. Find the value of ? so that the vectors ? ? ? ? 2 4 4 8 i j k and i j k ? - + - + ? ? are (i) parallel (ii) perpendicular [4] 8. Show that ? ? ( ) 1 2 3 6 7 a i j k = + + ? ? ? ( ) ? ? ( ) 1 1 6 2 3 3 6 2 7 7 b i j k c i j k = + - = - + ? ? [4] 9. If ? ? ? ? 3 2 2 2 4 a i j k b i j k = + + = - + ? ? find (i) Magnitude of a b × (ii) A unit vector ? a and b to both (iii) The cosine and cosine of the angle b w the vectors a and b [4] 10. The vectors ? ? ? ? 3 and 2 a i x j k b i j yk = + - = - + ? ? are mutually ? . Given , a b = find x and y [4]Read More

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