question_answer

The angle between two vector \[\overrightarrow{A}\And \overrightarrow{B}\] is \[\theta \]. vector \[\overrightarrow{R}\] is the resultant of vectors \[\overrightarrow{A}\And \overrightarrow{B},\] if \[\overrightarrow{R}\] makes an angle \[\frac{\theta }{2}\] with \[\overrightarrow{A}\] then

A) A = 2B

B) A = B/2

C) A = B

D) AB = 1

Correct Answer: C

Solution :

[c] From given situation vector diagram is drawn as shown in figure.

\[\angle ZXY+\angle YZX=\angle ZYU\] \[\Rightarrow \]\[\angle YZX=\frac{\theta }{2}\]

So XYZ is an isosceles triangle so \[|\overrightarrow{A}|=|\overrightarrow{B}|\]