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.

Integer / Numeric Answer Type