Page 1 CBSE TEST PAPER02 CLASS  XII MATHEMATICS (Vectors & Three Dimensional Geometry) Topic:  Vectors 1. Is the measure of 10 Newton is scalar or vector. [1] 2. Write two different vectors having same magnitude. [1] 3. Find the direction ratios and the direction cosines of the vector ? ? r i j k = + + ? [1] 4. Find 2, 3 . 4 a b if a b and a b  = = = [1] 5. If ? ? ? 4 3 2 3 2 2 a i j k b i k find b a = + + = + × ? ? [1] 6. Consider two point P and Q with position vectors 3 2 OP a b and OQ a b =  = + . Find the positions vector of a point R which divides the line joining P and Q in the ratio 2:1 (i) internally (ii) externally. [4] 7. Show that the points A, B, C with position vectors 2 3 5 , 2 3 7 a b c a b c and a c  + + + +  respectively are collinear. [4] 8. Find a unit vector ? to each of the vectors ( ) ( ) ? ? ? ? , 2 3 a b and a b where a i j k b i j k +  = + + = + + ? ? [4] 9. The scalar product of the vector ? ? i j k + + ? with a unit vector along the sum of vectors ? ? ? ? 2 4 5 , and 2 3 i j k i j k ? +  + + ? ? is equal the one. Find the value of ? [4] 10. Find the area of the ? with vertices A (1, 1, 2) B (2, 3, 5) and C (1, 5, 5). [4]Read More
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