Question

If the vectors $\overrightarrow{A}=2\hat{i}+4\hat{j}$ and $\overrightarrow{B}=5\hat{i}-p\hat{j}$ parallel to each other, the magnitude of $\overline{B}$ is:

• A. $5\sqrt{5}$
• B. 10
• C. 15
• D. $2\sqrt{5}$

Answer 1

Answer: (A)

$5\sqrt{5}$

Given vectors are :

$\overrightarrow{A}=2\hat{i}+4\hat{j}$

$\overrightarrow{B}=5\hat{i}-p\hat{j}$

$\overrightarrow{A}\parallel \overrightarrow{B}$

$\Rightarrow \frac{2}{5}=\frac{4}{-p}$

$\Rightarrow -2p=20$

$\Rightarrow p=-10$

$\overrightarrow{B}=5\hat{i}+10\hat{j}$

$\left|\overrightarrow{B}\right|=\sqrt{5^2+{10}^2}=\sqrt{125}=5\sqrt{5}$