JEE MAIN - Physics (2021 - 25th February Evening Shift - No. 20)
If $$\overrightarrow P \times \overrightarrow Q = \overrightarrow Q \times \overrightarrow P $$, the angle between $$\overrightarrow P $$ and $$\overrightarrow Q $$ is $$\theta$$(0$$^\circ$$ < $$\theta$$ < 360$$^\circ$$). The value of '$$\theta$$' will be ___________$$^\circ$$.
Answer
180
Explanation
Given, $$\overrightarrow P \times \overrightarrow Q = \overrightarrow Q \times \overrightarrow P $$
It is possible only when $$\overrightarrow P \times \overrightarrow Q = \overrightarrow Q \times \overrightarrow P $$ = 0
$$ \Rightarrow $$ We know, $$\overrightarrow P \times \overrightarrow Q $$ = PQsin $$\theta $$
Only if $$\overrightarrow P = 0$$
or $$\overrightarrow Q = 0$$
or sin $$\theta $$ = 0 $$ \Rightarrow $$ $$\theta $$ = 0 or 180o
The angle b/w $$\overrightarrow P $$ & $$\overrightarrow Q $$ is $$\theta$$(0$$^\circ$$ < $$\theta$$ < 360$$^\circ$$)
So, $$\theta$$ = 180$$^\circ$$
It is possible only when $$\overrightarrow P \times \overrightarrow Q = \overrightarrow Q \times \overrightarrow P $$ = 0
$$ \Rightarrow $$ We know, $$\overrightarrow P \times \overrightarrow Q $$ = PQsin $$\theta $$
Only if $$\overrightarrow P = 0$$
or $$\overrightarrow Q = 0$$
or sin $$\theta $$ = 0 $$ \Rightarrow $$ $$\theta $$ = 0 or 180o
The angle b/w $$\overrightarrow P $$ & $$\overrightarrow Q $$ is $$\theta$$(0$$^\circ$$ < $$\theta$$ < 360$$^\circ$$)
So, $$\theta$$ = 180$$^\circ$$
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