# Find the projection of the vector $$\hat i + \hat j + \hat k$$ on the vector $\hat j$.

Toolbox:
• Projection of $\overrightarrow a$ on $\overrightarrow b$ is $\large\frac{\overrightarrow a.\overrightarrow b}{|\overrightarrow b|}$
Step 1:
Let $\overrightarrow a=\hat i+\hat j+\hat k$ and $\overrightarrow b=\hat j$.
Projection of $\overrightarrow a$ on $\overrightarrow b$ is $\large\frac{\overrightarrow a.\overrightarrow b}{|\overrightarrow b|}$
Step 2:
Let us find $\overrightarrow a.\overrightarrow b$
$\overrightarrow a.\overrightarrow b=(\hat i+\hat j+\hat k).(\hat j)$
$\qquad =1$
Step 3:
Next we have to find $\mid\overrightarrow b\mid=1$
Step 4:
Projection of $\overrightarrow a$ on $\overrightarrow b$ is $\large\frac{\overrightarrow a.\overrightarrow b}{|\overrightarrow b|}$
$\overrightarrow a.\overrightarrow b=1$ and $\mid \overrightarrow b\mid=1$
$\Rightarrow \large\frac{1}{1}$$=1$
Hence the projection of $\overrightarrow a$ on $\overrightarrow b$ is $1$
edited Mar 20, 2014