Question

Find the unit vector in the direction of vector AB if the position vectors of A, B are 2i + 4j - k, 4i +5j + k

Answer 1

Given

vector OA = 2i + 4j - k, vector OB = 4i + 5j + k

vector AB= vector OB - vector OA

= (4i + 5j + k) - (2i + 4j - k)

= 2i + j + 2k

Required unit vector = vector AB/AB

= (2i + j + 2k)/√(4+1+4)

= (2i + j +2k)/3.