First slide

Vectors

Question

Two l vectors having equal magnitude , have a resultant equal to either of the two. The angle between them is

Moderate

A

90°
B

60°
C

120°
D

0°

Solution

Let two vectors are A and B, inclined at an angle $θ$ .

Resultant of the two vectors A and B,
$| R | = \sqrt{| A |^{2} + | B |^{2} + 2 | A | | B | \cos θ}$
Let $| A | = | B | = a$
According to the question, $|R| = a$
From Eq. (i), we get
$a = \sqrt{a^{2} + a^{2} + 2 a a \cos θ}$
$\Rightarrow a^{2} = a^{2} + a^{2} + 2 a^{2} \cos θ$
$\Rightarrow 2 a^{2} \cos θ = - a^{2}$
$\Rightarrow \cos θ = - 1 / 2$
$\Rightarrow θ = 120 °$

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