Question

Two vectors $A=3$ and $B=4$ are perpendicular. Resultant of both these vectors is $R$. The projection of the vector $B$ on the vector $R$ is

• A. $5$
• B. $1.25$
• C. $3.2$
• D. $2.4$

Answer 1

Answer: (C)

$3.2$

Let $\overrightarrow{A}=3\hat{i}$ and $\overrightarrow{B}=4\hat{j}$ because both are perpendicular.

Now,

$R=3\hat{i}+4\hat{j}$

Projection of $\overrightarrow{B}$ on $\overrightarrow{R}=\frac{\overrightarrow{R}.\overrightarrow{B}}{|R|}$

$=\frac{(3\overrightarrow{i}+4\overrightarrow{j}).\left(4\overrightarrow{j}\right)}{\sqrt{3^3+4^2}}$

$=\frac{16}{5}$

$=3.2$

Hence, C is the correct option.