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)
