Two vectors a and b are at an angle of 60^o with each other. Thei… - Vidyadip

MCQ

Two vectors $\overrightarrow a $ and $\overrightarrow b $ are at an angle of $60^o$ with each other. Their resultant makes an angle of $45^o$ with $\overrightarrow a $ . If $|\overrightarrow b | = 2\,units$ then $|\overrightarrow a |$ is:-

A
$\sqrt 3$
✓
$\sqrt 3 - 1$
C
$\sqrt 3 + 1$
D
$\sqrt 3 / 2$

✓

Answer

Correct option: B.

$\sqrt 3 - 1$

b
The vectors make $60^{\circ}$ with each other, and the resultant vector makes $45^{\circ}$ with $a$ The other angle $=15^{\circ}$ Using the side rule;

$a / \sin 15=2 / \sin 45$

$a=2 \sin 15 / \sin 45$

$a=0.732$

$ \sqrt{3}-1$

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