Kinematics Question 454
Question: If $ {{\bar{a}}_1} $ and $ {{\bar{a}}_2} $ are two non-collinear unit vectors and $ |{{\bar{a}}_1}+{{\bar{a}}_2}|=\sqrt{3}, $ then the value of $ ({{\bar{a}}_1}-{{\bar{a}}_2}).(2{{\bar{a}}_1}+{{\bar{a}}_2}) $ it’s
Options:
A) 2
B) 3/2
C) ½
D) 1
Correct Answer: C [c] $ | {{{\bar{a}}}_1}+{{{\bar{a}}}_2} |=\sqrt{a_1^{2}+a_2^{2}+2a_1a_2\cos \theta }=\sqrt{3} $ $ ({{\bar{a}}_1}-{{\bar{a}}_2})(2{{\bar{a}}_1}+{{\bar{a}}_2})=2a_1^{2}-a_2^{2}-a_1a_2\cos \theta =\frac{1}{2} $
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Answer:
Solution:
$ \Rightarrow $ $ \cos \theta =\frac{1}{2} $
