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Find a vector of magnitude 5 units, and parallel to the resultant of the vectors \( \overrightarrow a = 2\hat i + 3\hat j - \hat k \: and \: \overrightarrow b = \hat i - 2\hat j + \hat k\)

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  • Vector which is parallel with magnitude is $\pm \large\frac{\overrightarrow a+\overrightarrow b}{\mid \overrightarrow a+\overrightarrow b\mid}$
Step 1:
$\overrightarrow a=2\hat i+3\hat j-\hat k$
$\overrightarrow b= i-2\hat j+\hat k$
The resultant vector is $\overrightarrow a+\overrightarrow b=(2\hat i+3\hat j-\hat k+\hat i-2\hat j+\hat k)$
$\Rightarrow 3\hat i+\hat j$
Step 2:
Vector which is parallel to the above with magnitude 5 is $\pm \large\frac{\overrightarrow a+\overrightarrow b}{\mid \overrightarrow a+\overrightarrow b\mid}$
$\Rightarrow \pm\large\frac{(3\hat i+\hat j}{\sqrt{3^2+1^2}}$
$\Rightarrow \pm\large\frac{(3\hat i+\hat j}{\sqrt{10}}$
$\Rightarrow \pm\large\frac{\sqrt{10}}{2}$$(3\hat i+\hat j)$
answered Dec 2, 2013 by sreemathi.v

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