Question

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

Column I		Column II
(a)	| A × B | = 0	(i)	θ = 30º
(b)	| A × B | = +8	(ii)	θ = 45º
(c)	| A × B | = 4	(iii)	θ = 90º
(d)	| A × B | = −8	(iv)	θ = 0º

Answer 1

(a) --- (iv) because sin θ = 0º , hence | A | | B | sin0 = 2×4×0 = 0

(b) --- (iii) because sin 90º = 1, hence | A | | B | sin 90º = 2×4×1 = 8

(c) --- (i) because sin 30º = \(\frac{1}{2}\) , hence | A | | B | sin 30º = 2×4× \(\frac{1}{2}\) = 4 

(d) ---  (ii) because sin 45º = \(\frac{1}{\sqrt 2}= \frac{\sqrt 2}{2}\) , hence, | A | | B | sin 45º = 2×4×\(\frac{\sqrt 2}{2}=4\sqrt2\)