Browse Questions

Find the projection of $\overrightarrow a \: on \: \overrightarrow b\: if \: \overrightarrow a.\overrightarrow b=8\: and \: \overrightarrow b = 2\hat i + 6\hat j + 3\hat k$

Toolbox:
• Projection of $\overrightarrow a$ and $\overrightarrow b$ is given by $\large\frac{\overrightarrow a.\overrightarrow b}{\mid \overrightarrow b\mid}$
Step 1:
Given :
$\overrightarrow a.\overrightarrow b=8$
$\overrightarrow b=2\hat i+6\hat j+3\hat k$
Projection of $\overrightarrow a$ on $\overrightarrow b$ is $\large\frac{\overrightarrow a.\overrightarrow b}{\mid \overrightarrow b\mid}$
$\mid \overrightarrow b\mid =\sqrt{(2)^2+(6)^2+(3)^2}$
$\qquad=\sqrt{4+36+9}$
$\qquad=\sqrt{49}$
$\qquad=7$
Step 2:
$\therefore$Projection of $\overrightarrow a$ on $\overrightarrow b=\large\frac{8}{7}$