# Write two different vectors having same magnitude.

Toolbox:
• Two vectors can have same magnitude,if their lengths are equal.
Step 1:
Consider a vector $\overrightarrow{a}=\hat i+\hat{j}+\hat k$ and $\overrightarrow{b}=\hat i-\hat j-\hat k$.
Now let us compute the magnitude of $\overrightarrow{a}$
$\mid \overrightarrow{a}\mid=\sqrt{1^2+1^2+1^2}$
$\qquad=\sqrt{3}$
Hence $\mid \overrightarrow a\mid=\sqrt{3}$
Step 2:
Next let us compute the magnitude of $\overrightarrow{b}$
$\mid \overrightarrow{b}\mid=\sqrt{1^2+(-1)^2+(-1)^2}$
$\qquad=\sqrt{1^2+1^2+1^2}$
$\qquad=\sqrt{3}$
Hence $\mid \overrightarrow b\mid=\sqrt{3}$
Step 3:
Therefore $\overrightarrow{a}$ and $\overrightarrow{b}$ are having same magnitude .
Hence $\overrightarrow{a}=\hat i+\hat j+\hat k$ and $\overrightarrow{b}=\hat{i}-\hat j-\hat k$ are two vectors which are equal in magnitude.
answered May 16, 2013