Vectors 2 Question 15
15. If the triangle $P Q R$ varies, then the minimum value of $\cos (P+Q)+\cos (Q+R)+\cos (R+P)$ is
(a) $-\frac{3}{2}$
(b) $\frac{3}{2}$
(c) $\frac{5}{3}$
(d) $-\frac{5}{3}$
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Answer:
Correct Answer: 15. $\vec{a}$
Solution:
- $\cos (P+Q)+\cos (Q+R)+\cos (R+P)$
$$ =-(\cos R+\cos P+\cos Q) $$
Max. of $\cos P+\cos Q+\cos R=\frac{3}{2}$
Min. of $\cos (P+Q)+\cos (Q+R)+\cos (R+P)$ is $=-\frac{3}{2}$
