Question 34: Motion in 2D & Vectors

Question

If $$\overrightarrow P  	imes \overrightarrow Q  = \overrightarrow Q  	imes \overrightarrow P $$, the angle between $$\overrightarrow P $$ and $$\overrightarrow Q $$ is $$	heta$$(0$$^\circ$$ < $$	heta$$ < 360$$^\circ$$). The value of '$$	heta$$' will be ___________$$^\circ$$.

Accepted Answer

Given, $$\overrightarrow P  	imes \overrightarrow Q  = \overrightarrow Q  	imes \overrightarrow P $$
It is possible only when $$\overrightarrow P  	imes \overrightarrow Q  = \overrightarrow Q  	imes \overrightarrow P $$ = 0
$$ \Rightarrow $$ We know, $$\overrightarrow P  	imes \overrightarrow Q $$ = PQsin $$	heta $$
Only if $$\overrightarrow P  = 0$$
or $$\overrightarrow Q  = 0$$
or sin $$	heta $$ = 0 $$ \Rightarrow $$ $$	heta $$ = 0 or 180
o
The angle b/w $$\overrightarrow P $$ & $$\overrightarrow Q $$ is $$	heta$$(0$$^\circ$$ < $$	heta$$ < 360$$^\circ$$)
So, $$	heta$$ = 180$$^\circ$$

Motion in 2D & Vectors

If $\overrightarrow P \times \overrightarrow Q = \overrightarrow Q \times \overrightarrow P , the angle between \overrightarrow P and \overrightarrow Q is \theta(0^\circ < \theta < 360^\circ). The value of '\theta' will be ___________^\circ$.

Choose the correct answer: