Question
Find the unit vector in the direction of the vector $\vec a = \hat i + \hat j + 2\hat k$
$\hat a = \frac{{\vec a}}{{\left| {\vec a} \right|}} = \frac{{\hat i + \hat j + 2\hat k}}{{\sqrt {{1^2} + {1^2} + {2^2}} }} = \frac{{\hat i + \hat j + 2\hat k}}{{\sqrt {1 + 1 + 4} }} = \frac{{\hat i + \hat j + 2\hat k}}{{\sqrt 6 }}$
$\Rightarrow \hat a = \frac{1}{{\sqrt 6 }}\hat i + \frac{1}{{\sqrt 6 }}\hat j + \frac{2}{{\sqrt 6 }}\hat k$
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| Differential equation | Function |
| $\text{x}\frac{\text{dy}}{\text{dx}}=\text{y}$ | $\text{y}=\text{ax}$ |