Question

ABCD is a parallelogram. The position vectors of A, B and C are given respectively by

vector a = 2i + j + 3k, vector b = 3i - 2j vector c = i - j - 2k

(i) Find the position vector of D.

(ii) Determine, to the nearest degree, the angle ABC.

Answer 1

(i) OD = OA + AD or OB + BC + CD AEF

AD = BC or CD = BA

vector OD = 2i + k

(ii) AB.CB = |AB||CB| cosθ ⇒ cosθ = 86°