Motion in a Plane - Result Question 14
16. The angle between two vectors of magnitude 12 and 18 units when their resultant is 24 units, is
(a) $63^{\circ} 51^{\prime}$
(b) $75^{\circ} 52^{\prime}$
(c) $82^{\circ} 31^{\prime}$
(d) $89^{\circ} 16^{\prime}$
[1999]
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Answer:
Correct Answer: 16. (b)
Solution:
- (b) We know that, $R^{2}=A^{2}+B^{2}+2 A B \cos \theta$ $(24)^{2}=(12)^{2}+(18)^{2}+2(12)(18) \cos \theta$
$\cos \theta=\frac{108}{432} \Rightarrow \theta=75^{\circ} 52^{\prime}$
