Question

Which of the following is a unit vector along $3i-2j$ ?

• A. $-\frac{3}{\sqrt{5}}i+\frac{2}{\sqrt{5}}j$
• B. $\frac{3}{\sqrt{13}}i+\frac{2}{\sqrt{13}}j$
• C. $-\frac{3}{\sqrt{5}}i-\frac{2}{\sqrt{5}}j$
• D. $\frac{3}{\sqrt{13}}i-\frac{2}{\sqrt{13}}j$

Answer 1

The correct option is D $\frac{3}{\sqrt{13}}i-\frac{2}{\sqrt{13}}j$

Given: $3i-2j$
A unit vector along any vector can be found out by dividing the vector with the magnitude of the vector.
$\Rightarrow \frac{3i-2j}{\sqrt{3^2+(-2{)}^2}}=\frac{3i-2j}{\sqrt{13}}$
$\Rightarrow \frac{3}{\sqrt{13}}i-\frac{2}{\sqrt{13}}j$