Page 1 CBSE TEST PAPER01 CLASS  XII MATHEMATICS (Vectors & Three Dimensional Geometry) Topic:  Vectors 1. Is the measure of 5 seconds is scalar or vector? [1] 2. Find the sum of the vectors. ? ? 2 , 2 4 5 6 7 a i j k b i j k c i j k =  + =  + + =   ? [1] 3. Find the direction ratios and the direction cosines of the vector ? ? 2 7 3 r i j k =   ? [1] 4. Find the angle between vectors 3, 2 . 6 a and b if a b a b = = = [1] 5. Vectors a and b be such that 2 3, , 3 a and b = = then a b × is a unit vector. Find angle between a and b . [1] 6. Find the unit vector in the direction of the sum of the vectors ? ? ? ? 2 2 5 , 2 3 a i j k b i j k = +  = + + ? ? [4] 7. Show that the points ? ? ( ) ? ? ( ) ? ? ( ) 2 , 3 5 , 3 4 4 A i j k B i j k C i j k  +     ? ? ? are the vertices of right angled triangle. [4] 8. Show that the points ? ? ( ) ? ? ( ) ? ( ) 2 3 5 , 2 3 7 A i j k B i j k and C i k  + + + +  ? ? ? are collinear. [4] 9. If , , a b c are unit vector such that 0 a b c + + = find the value of . . . a b b c c a + + [4] 10. If ? ? ? ? ? 2 2 3 , 2 , 3 a i j k b i j k c i j = + + =  + + = + ? ? ? are such that a b is to c ? + ? is then find the value of ? . [4]Read More
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