First slide

Scalars and Vectors

Question

If $|{\vec{V}}_{1} + {\vec{V}}_{2}| = |{\vec{V}}_{1} - {\vec{V}}_{2}| and V_{2}$ is finite, then

Moderate

A

$V_{1} is parallel to V_{2}$
B

${\vec{V}}_{1} = {\vec{V}}_{2}$
C

$V_{1} and V_{2} are mutually perpendicular$
D

$|{\vec{V}}_{1}| = |{\vec{V}}_{2}|$

Solution

According to problem $|{\vec{V}}_{1} + {\vec{V}}_{2}| = |{\vec{V}}_{1} - {\vec{V}}_{2}|$
$\Rightarrow \sqrt{V_{1}^{2} + V_{2}^{2} + 2 V_{1} V_{2} \cos θ} = \sqrt{V_{1}^{2} + V_{2}^{2} - 2 V_{1} V_{2} \cos θ}$
$\Rightarrow \cos θ = 0$
$\Rightarrow θ = 90^{0}$
$So V_{1} and V_{2} will be mutually perpendicular.$
$\begin{array}{l} A l s o, |{\vec{V}}_{net}| = |{\vec{V}}_{net}^{'}| \end{array}$

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