Find direction ratio and the direction cosines of the vector $\to r =^i +^j +^k$ .

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Solution

Let $\to r = ˆ i + ˆ j + ˆ k$
$= 1 ˆ i + 1 ˆ j + 1 ˆ k$
Direction ratios are
a=1, b=1, c=1
Magnitude of $\begin{matrix} \to r = \sqrt{1^{2} + 1^{2} + 1^{2}} ∣ ∣ \to r ∣ ∣ = \sqrt{3} \end{matrix}$
Direction cosines are
$⎛ ⎜ ⎝ \frac{a}{∣ ∣ \to a ∣ ∣}, \frac{b}{∣ ∣ \to a ∣ ∣}, \frac{c}{∣ ∣ \to a ∣ ∣} ⎞ ⎟ ⎠$
Direction cosines of $\to a = (\frac{1}{\sqrt{3}}, \frac{1}{\sqrt{3}}, \frac{1}{\sqrt{3}})$

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