Question

If$\overrightarrow{u}=3\hat{i}-5\hat{j}+9\hat{k}and\overrightarrow{v}=3\hat{i}+4\hat{j}+0\hat{k}$ , then the component of u along the direction of v is

• A. $\frac{-11}{5}$
• B. $\frac{-11}{7}$
• C. $\frac{11}{5}$

Answer 1

The correct option is A $\frac{-11}{5}$

Component of $\overrightarrow{u}$ along the direction of $\overrightarrow{v}$ can be calculated using dot product.
We know,
$\overrightarrow{u}.\overrightarrow{v}=|u||v|cos\theta$
$\Rightarrow (9-20+0)=\left(\sqrt{(3{)}^2+(5{)}^2+(9{)}^2}\right)\left(\sqrt{(3{)}^2+(4{)}^2+(0{)}^2}\right).cos\theta$
$cos\theta =\frac{-11}{\sqrt{115}\times 5}$
The component of $\overrightarrow{u}$ along the direction of $\overrightarrow{v}$ will be = $|u|$ cos $\theta$
$|u|=\sqrt{115}$
$\Rightarrow |u|.cos\theta =\frac{-11}{5}$