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Home  >>  CBSE XII  >>  Math  >>  Vector Algebra
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Find the projection of the vector \( \hat i − \hat j\) on the vector \( \hat i + \hat j .\)

$\begin{array}{1 1} 0 \\ \sqrt 2 \\ 1 \\ 2 \end{array} $

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  • Projection of $ \overrightarrow a\: on \: \overrightarrow b$ is $ \large\frac{\overrightarrow a.\overrightarrow b}{|\overrightarrow b |}$
Step 1:
Let $\overrightarrow a=\hat i-\hat j$ and $\overrightarrow b=\hat i+\hat j$.
Projection of $ \overrightarrow a\: on \: \overrightarrow b$ is given by $ \large\frac{\overrightarrow a.\overrightarrow b}{|\overrightarrow b |}$
$\overrightarrow a.\overrightarrow b=(\hat i-\hat j).(\hat i+\hat j)$
$\qquad\;=1-1=0$
$\mid \overrightarrow b\mid=\sqrt{1^2+1^2}$
$\mid \overrightarrow b\mid=\sqrt{2}$
Step 2:
Projection of $\overrightarrow a$ on $\overrightarrow b$ is $\large\frac{0}{\sqrt{2}}$
Projection of $\overrightarrow a$ on $\overrightarrow b$ is 0.
answered May 20, 2013 by sreemathi.v
 

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