Question

If $\overrightarrow{a}$ is a vector of magnitude 50 and is collinear with the vector $\overrightarrow{b}=6\hat{i}-8\hat{j}-\frac{15}{2}\hat{k}$ and makes an obtuse angle with the positive direction of z - axis, then $\overrightarrow{a}$ is equal to

• A. $24\hat{i}-32\hat{j}-30\hat{k}$
• B. $24\hat{i}+32\hat{j}+30\hat{k}$
• C. $12\hat{i}-16\hat{j}-15\hat{k}$
• D. $12\hat{i}-43\hat{j}-15\hat{k}$

Answer 1

The correct option is A $24\hat{i}-32\hat{j}-30\hat{k}$

Since, $\overrightarrow{a}$ is collinear to vector $\overrightarrow{b}$, therefore $\overrightarrow{a}=m\overrightarrow{b}$ for some scalar m ie,
$\overrightarrow{a}=m(6\hat{i}-8\hat{j}-\frac{15}{2}\hat{k})\Rightarrow |\overrightarrow{a}|=|m|\sqrt{36+64+\frac{225}{4}}=\frac{25}{2}|m|\Rightarrow 50=\frac{25}{2}|m|\Rightarrow |m|=4$
$\Rightarrow m=\pm 4[\because |\overrightarrow{a}|=50]$