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24 Nov 2011 06:12:47 IST

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Doubts form FIITJEE Pckg

Mathematics

Doubts From VECTOR ALGEBRA (fiitjee pckg)Q.1. In a Triangle ABC, the bisector of angle A meets the opposite side at D. Using vectors Prove that BD : DC = c : b.Q.2. The vector (-1,1,1) bisects the angle between the vectors C(x,y,z) and (3,4,0). determine a unit vector along C(x,y,z).Q.3. If a, b, c and a', b', c' are reciprocal system of vectors , then prove that: a' x b' + b' x c' + c' x a' = (a + b+ c)/[a b c]Q.4.Prove necessary and sufficient condition for a x (b x c) = (a x b) x c is that (a x c) x b = 0.*note in question 3,4 consider a vector sign above the letters a,b,c,a',b',c'. since they are vectors and close bracket [ ] implies scalar triple product of vectors. Moreover 'x' implies Cross Product.(Questions from FIITJEE Package-Vectors Assignment Level 2)

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