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 $