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

For two vectors a→\overset{\rightarrow}{a}andb→\overset{\rightarrow}{b}, if R→\overset{\rightarrow}{R}= a→\overset{\rightarrow}{a} + b→\overset{\rightarrow}{b} and S→\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 toa→\overset{\rightarrow}{a}, then –

A

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

37\sqrt{\frac{3}{7}}

Explanation

Solution

As R→\overset{\rightarrow}{R} is perpendicular to a→\overset{\rightarrow}{a} therefore

cos q =−ab\frac{- a}{b}Ž R =b2−a2\sqrt{b^{2} - a^{2}} and S =3a2+b2\sqrt{3a^{2} + b^{2}}

As 2 |R→\overset{\rightarrow}{R}| = |S→\overset{\rightarrow}{S}|

Ž 4b2 – 4a2 = 3a2 + b2 Ž 3b2 = 7a2