Question

Consider two vector $\overrightarrow{F_1}=2\hat{i}+5\hat{k}$ and $\overrightarrow{F_2}=3\hat{j}+4\hat{k}$. The magnitude of the dot product of these vector is

• A. $20$
• B. $23$
• C. $5\sqrt{33}$
• D. $26$

Answer 1

The correct option is A $20$

$\text{Given:-}$ $F_1=2\hat{i}+5\hat{k}$

$F_2=3\hat{j}+4\hat{k}$

$\text{Solution:-}$

We know that ,

Scalar product $=\overrightarrow{F_1}\cdot \overrightarrow{F_2}$

$=(2\hat{i}+5\hat{k})\cdot (3\hat{j}+4\hat{k})$

$=(2\hat{i}+0\hat{j}+5\hat{k})\cdot (0\hat{i}+3\hat{j}+4\hat{k})$

$=0+0+20$

$=20$

$\text{Hence the correct option is A}$