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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 = 0 |
| (b) A.B = + 8 | (ii) θ = 90° |
| (c) A.B = 4 | (iii) θ = 180° |
| (d) A.B = – 8 | (iv) θ = 60° |
Solution
| Column I | Column II |
| (a) A.B = 0 | (ii) θ = 90° |
| (b) A.B = + 8 | (i) θ = 0 |
| (c) A.B = 4 | (iv) θ = 60° |
| (d) A.B = – 8 | (iii) θ = 180° |
Explanation:
Given |A| = 2 and |B| = 4
(a) A.B = AB cos θ = 0
⇒ 2 × 4 cos θ = 0
⇒ cos θ = 0 = cos 90°
⇒ θ = 90°
(b) A.B = AB cos θ = 8
⇒ 2 × 4 cos θ = 8
⇒ cos θ = 1 = cos 0°
⇒ θ = 0°
(c) A.B = AB cos θ = 4
⇒ 2 × 4 cos θ = 4
⇒ cos θ = `1/2` = cos 60°
⇒ θ = 60°
(d) A.B = AB cos θ = – 8
⇒ 2 × 4 cos θ = – 8
⇒ cos θ = – 1 = cos 180°
⇒ θ = 180°
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