Question

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

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

Answer 1

The correct option is B -10

For a vector to be parallel to another vector there will be $a=ub$ where $a$ is constant and $b$ is vector and vector $u$ is any real constant. Now for above equation $2i+4j=4(5i-pj)$

Compare the vector separately $u=\frac{2}{5}$

Putting value of $u$ where $u$ is with $p$

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

$p=-4\times \frac{5}{2}=-10$.