Question

If | A | = 2 and | B | = 4, then match the relations in column with the angle θ between A and B in column .

Column		Column
(a)	A.B = 0	(i)	θ = 0
(b)	A.B = +8	(ii)	θ = 90º
(c)	A.B = 4	(iii)	θ = 180º
(d)	A.B = −8	(iv)	θ = 60º

Answer 1

(a) (ii) because cos 90º = 0, hence | A | | B | cos 90º = 2×4×\(\frac{1}{2}\) = 0

(b) (i) because cos 0º = 1, hence A | | B | cos 0º = 2×4×1 = +8

(c) (iv) because cos 60º = \(\frac{1}{2}\), hence | A | | B | cos 60º = 2×4× \(\frac{1}{2}\) = +4

(d) (iii) because cos 180º = −1, hence | A | | B | cos 180º = 2×4×−1 = −8