Question
Find the vector in the direction of vector $2\hat{\text{i}}-3\hat{\text{j}}+6\hat{\text{k}}$ which has magnitude 21 units.
✓
Answer
Let $\vec{\text{a}}=2\hat{\text{i}}-3\hat{\text{j}}+6\hat{\text{k}}$
$\therefore\ |\vec{\text{a}}|=\sqrt{2^2+(-3)^2+6^2}$
$=\sqrt{4+9+36}$
$=\sqrt{49}$
$=7$
Unit vector in the direction of $\vec{\text{a}}=\frac{\vec{\text{a}}}{|\vec{\text{a}}|}=\frac{2\hat{\text{i}}-3\hat{\text{j}}+6\hat{\text{k}}}7$
$\therefore$ vector in the direction of vector $\vec{\text{a}}$ which has magnitude 21 units
$=21\times\Big(\frac{2\hat{\text{i}}-3\hat{\text{j}}+6\hat{\text{k}}}7\Big)$
$=3\big(2\hat{\text{i}}-3\hat{\text{j}}+6\hat{\text{k}}\big)$
$=6\hat{\text{i}}-9\hat{\text{j}}+18\hat{\text{k}}$
$\therefore\ |\vec{\text{a}}|=\sqrt{2^2+(-3)^2+6^2}$
$=\sqrt{4+9+36}$
$=\sqrt{49}$
$=7$
Unit vector in the direction of $\vec{\text{a}}=\frac{\vec{\text{a}}}{|\vec{\text{a}}|}=\frac{2\hat{\text{i}}-3\hat{\text{j}}+6\hat{\text{k}}}7$
$\therefore$ vector in the direction of vector $\vec{\text{a}}$ which has magnitude 21 units
$=21\times\Big(\frac{2\hat{\text{i}}-3\hat{\text{j}}+6\hat{\text{k}}}7\Big)$
$=3\big(2\hat{\text{i}}-3\hat{\text{j}}+6\hat{\text{k}}\big)$
$=6\hat{\text{i}}-9\hat{\text{j}}+18\hat{\text{k}}$
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