Question

Let vector a = - i - k, vector b = i + 2j and vector c = i + 2j + 3k be three given vectors. If r is a vector such that vector(r x b) = vector(c x b) and vector (r. a) = 0  then the value of vector (r. b) is 

Answer 1

Vector(r x b) = vector(c x b)

Taking cross with a

⇒ vector(a x (r x b)) = vector(a x (c x b))

⇒ vector((a x b)r - (a x r)b) = vector(a x (c x b))

⇒ vector r = - 3i + 6j + 3k

vector(r x b) = 3 + 6 = 9