Question

If the vector $8\hat{i}+a\hat{j}$ of magnitude $10$ is in the direction of the vector $4\hat{i}-3\hat{j},$ then the value of a is equal to

• A. 6
• B. 3
• C. $-3$
• D. 5
• E. $-6$

Answer 1

Answer: (E)

Since, the vector $8i+aj$ in the direction of the vector $4i-3j$ . That means both vectors are parallel to each other. By condition of parallel vectors, $\frac{8}{4}=\frac{a}{-3}$
$\Rightarrow$ $a=-6$ Alternative Method Given also, $|8i+aj|=10$
$\Rightarrow$ $\sqrt{64+a^2}=10$
$\Rightarrow$ $64+a^2=100$
$\Rightarrow$ $a^2=36$
$\Rightarrow$ $a=\pm 6$ (here we take (-) ve sign)
$\Rightarrow$ $a=-6$