Question

The resultant of $\left(p-2q\right)$ where $p=7i-2j+3k$ and $q=3i+j+5k$ is?

• A. $\sqrt{29}$
• B. $4$
• C. $\sqrt{66}-2\sqrt{35}$
• D. $\sqrt{66}$

Answer 1

The correct option is D

$\sqrt{66}$

Explanation for the correct option:

Find the resultant of given expression

Given,

$p=7i-2j+3k$

$q=3i+j+5k$

Therefore

$$\begin{gathered} p-2q=7i-2j+3k-2\left(3i+j+5k\right) \\ \Rightarrow p-2q=7i-2j+3k-6i-2j-10k \\ \Rightarrow p-2q=i-4j-7k \end{gathered}$$

Now the resultant of $\left(p-2q\right)$ is

$$\begin{gathered} \left|p-2q\right|=\sqrt{1^2+{\left(-4\right)}^2+{\left(-7\right)}^2} \\ =\sqrt{1+16+49} \\ =\sqrt{66} \end{gathered}$$

Hence, the correct option is $\left(\mathrm{D}\right)$.