Question

If $u=3\hat{i}-5\hat{j}+9\hat{k}andv=3\hat{i}+4\hat{j}+0k;$ What is the component of u along the direction of v?

• A.
• B.
• C.
• D.

Answer 1

The correct option is B

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