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Question: For two vectors \(\overset{\rightarrow}{a}\)and \(\overset{\rightarrow}{b}\), if \(\overset{\rightar...

For two vectors a→\overset{\rightarrow}{a}and b→\overset{\rightarrow}{b}, if R→\overset{\rightarrow}{R}=a→\overset{\rightarrow}{a}+b→\overset{\rightarrow}{b}andS→\overset{\rightarrow}{S}=a→\overset{\rightarrow}{a}–b→\overset{\rightarrow}{b}, If 2|R→\overset{\rightarrow}{R}|=|S→\overset{\rightarrow}{S}| when R→\overset{\rightarrow}{R} is perpendicular to a→\overset{\rightarrow}{a}, then –

A

ab\frac{a}{b} =37\sqrt{\frac{3}{7}}

B

ab\frac{a}{b} =73\sqrt{\frac{7}{3}}

C

ab\frac{a}{b} =15\sqrt{\frac{1}{5}}

D

ab\frac{a}{b}=51\sqrt{\frac{5}{1}}

Answer

ab\frac{a}{b} =37\sqrt{\frac{3}{7}}

Explanation

Solution

Use R = a2+b2+2abcos⁡θ\sqrt{a^{2} + b^{2} + 2ab\cos\theta} and

S = a2+b2−2abcos⁡θ\sqrt{a^{2} + b^{2} - 2ab\cos\theta}

also tan a = bsin⁡θa+bcos⁡θ\frac{b\sin\theta}{a + b\cos\theta}