Question

If $p=i+j,q=4k-j,\text{and}r=i+k$ then the unit vector in the direction of $3p+q-2r$ is?

• A. $\frac{1}{3}\left(i+2j+2k\right)$
• B. $\frac{1}{3}\left(i-2j-2k\right)$
• C. $\frac{1}{3}\left(i-2j+2k\right)$
• D. $\left(i+2j+2k\right)$

Answer 1

The correct option is A

$\frac{1}{3}\left(i+2j+2k\right)$

Explanation for the correct option

First calculate the value of $3p+q-2r$, then find unit vector.

Apply the value of $p,q$ and $r$ in $3p+q-2r$, we have

$\begin{array}{rcl}3p+q-2r& =& 3\left(i+j\right)+\left(4k-j\right)-2\left(i+k\right)\\ & =& 3i+3j+4k-j-2i-2k\\ & =& i+2j+2k\end{array}$

Since, we know that, $unitvector=\frac{vector}{\left|vector\right|}$

Therefore, the unit vector in direction of $3p+q-2r$ will be

$3p+q-2r=\frac{\left(i+2j+2k\right)}{\left|\left(i+2j+2k\right)\right|}=\frac{\left(i+2j+2k\right)}{\sqrt{1+4+4}}=\frac{\left(i+2j+2k\right)}{3}\begin{array}{}\end{array}$

Hence, the correct option is (A).