Question

Vector $\overrightarrow{a}$ has components $a_x=3,a_y=4$. Find the components of a vector $\overrightarrow{c}$ which is perpendicular to $\overrightarrow{a}$ and has a magnitude of $5$ units.

• A. $c_x=\pm 4,c_y=\mp 3$
• B. $c_x=\pm 3,c_y=\mp 4$
• C. $c_x=\pm 2,c_y=\mp 3$
• D. $c_x=\pm 3,c_y=\mp 2$

Answer 1

The correct option is A $c_x=\pm 4,c_y=\mp 3$

Let $\overrightarrow{c}$ is $=c_x\hat{i}+c_y\hat{j}$

Then, according to question $=\sqrt{c_x^2+c_y^2}=5$

$\Rightarrow c_x^2+c_y^2=25....\left(i\right)$

and $\overrightarrow{a}.\overrightarrow{c}=0\Rightarrow 3c_x+4c_y=0.....\left(ii\right)$

Form equation (i) and (ii):

$c_x=\pm 4,c_y=\mp 3$