Question

The position vectors of three points A, B and C relative to an origin O are given respectively by vector OA = 7i + 3j - 3k, vector OB = 4i + 2j - 4k, vector OC = 5i + 4j + 5k. 

(i) Find the angle between AB and AC. 

(ii) Find the area of triangle ABC.

Answer 1

(i) Work out vector (b - a) or vector(a - b)  or vector (c - a)  or vector (a - c)

= ± ( -3i - j - k) or ±( -2i + j - 2k)

Use cosine rule and find angle as o 45.3°

(ii) Use of 1/2|vector AB| x |vector AC|sinθ

= 1/2(√11)(3)sin45.3° = 3.54