Question

Refer to the following figure and find the option(s) with correct descriptions about the vectors given in the figure.

• A. $\underset{a}{\to }$ = $\underset{-b}{\to }$
• B. $\underset{a}{\to }$ = $\underset{-c}{\to }$
• C. $\underset{c}{\to }$ = $\underset{-d}{\to }$
• D. $\underset{b}{\to }$ = $\underset{-d}{\to }$

Answer 1

Answer: (A), (C)

The correct options are
A $\underset{a}{\to }$ = $\underset{-b}{\to }$
C $\underset{c}{\to }$ = $\underset{-d}{\to }$

Negative of a vector $\underset{u}{\to }$ is a vector having the same magnitude but the opposite direction.
Here
$\left|\underset{a}{\to }\right|=\left|\underset{b}{\to }\right|$

But $\underset{a}{\to }$ is in opposite direction of $\underset{b}{\to }$
So $\underset{a}{\to }=\underset{-b}{\to }$
Similarly
$\left|\underset{c}{\to }\right|=\left|\underset{d}{\to }\right|$

So $\underset{c}{\to }=\underset{-d}{\to }$
$\underset{a}{\to }$ and $\underset{c}{\to }$ are not in opposite directions. So $\underset{a}{\to }\ne \underset{-c}{\to }$
Same is the case with $\underset{b}{\to }and\underset{d}{\to }$