Question 59: Motion in 2D & Vectors

Question

The angle between vector $$\left( {\overrightarrow A } \right)$$ and $$\left( {\overrightarrow A  - \overrightarrow B } \right)$$ is :

Accepted Answer

Angle between $${\overrightarrow A }$$ and $${\overrightarrow B }$$, $$	heta$$ = 60$$^\circ$$
Angle between $${\overrightarrow A }$$ and -$${\overrightarrow B }$$, $$	heta$$ = 120$$^\circ$$
If angle between $${\overrightarrow A }$$ and $${\overrightarrow A }$$ $$-$$ $${\overrightarrow B }$$ is $$\alpha $$
then $$	an \alpha  = $$$${{\left| { - \overrightarrow B } ight|\sin 	heta } \over {\overrightarrow A  + \left| { - \overrightarrow B } ight|\cos 	heta }}$$
= $${{B\sin 120^\circ } \over {A + B\cos 120^\circ }}$$
=$${{B{{\sqrt 3 } \over 2}} \over {A - {B \over 2}}}$$
$$ \Rightarrow $$ $$	an \alpha  = {{\sqrt 3 B} \over {2A - B}}$$

Answer

$${	an ^{ - 1}}\left( {{{ - {B \over 2}} \over {A - B{{\sqrt 3 } \over 2}}}} ight)$$

Answer

$${	an ^{ - 1}}\left( {{A \over {0.7B}}} ight)$$

Answer

$${	an ^{ - 1}}\left( {{{\sqrt 3 B} \over {2A - B}}} ight)$$

Answer

$${	an ^{ - 1}}\left( {{{B\cos 	heta } \over {A - B\sin 	heta }}} ight)$$

Motion in 2D & Vectors

The angle between vector $\left( {\overrightarrow A } \right) and \left( {\overrightarrow A - \overrightarrow B } \right)$ is :

Choose the correct answer: