Question

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

Column I	Column II
(a) |A × B| = 0	(i) θ = 30°
(b) |A × B| = 8	(ii) θ = 45°
(c) |A × B| = 4	(iii) θ = 90°
(d) |A × B| = `4sqrt(2)`	(iv) θ = 0°

Answer 1

Column I	Column II
(a) |A × B| = 0	(iv) θ = 0°
(b) |A × B| = 8	(iii) θ = 90°
(c) |A × B| = 4	(i) θ = 30°
(d) |A × B| = `4sqrt(2)`	(ii) θ = 45°

Explanation:

Given |A| = 2 and |B| = 4

(a) |A × B| = AB sin θ = 0

⇒ 2 × 4 sin θ = 0

⇒ sin θ = 0 = sin 0°

⇒ θ = 0°

(b) |A × B| = AB sin θ = 8

⇒ 2 × 4 sin θ = 8

⇒ sin θ = 1 = sin 90°

⇒ θ = 90°

(c) |A × B| = AB sin θ = 4

⇒ 2 × 4 sin θ = 4

⇒ sin θ = `1/2` = sin 30°

⇒ θ = 30°

(d) |A × B| = AB sin θ = `4sqrt(2)`

⇒ 2 × 4 sin θ = `4sqrt(2)`

⇒ sin θ = `1/sqrt(2)` = sin 45°

⇒ θ = 45°