First slide

Scalars and Vectors

Question

If a vector $r = x \hat{i} + y \hat{j} + z \hat{k}$ , makes angle $\frac{π}{3}, \frac{π}{3} and \frac{π}{n}$ with X-axis, Y-axis and Z-axis respectively. The value of n is _______.

Moderate

Solution

$\begin{array}{l} \cos^{2} α + \cos^{2} β + \cos^{2} γ = 1 \\ or \cos^{2} 60^{\circ} + \cos^{2} 60^{\circ} + \cos^{2} γ = 1 \\ or \frac{1}{4} + \frac{1}{4} + \cos^{2} γ = 1 \\ or \cos^{2} γ = 1 - \frac{1}{2} = \frac{1}{2} \\ or \cos γ = \frac{1}{\sqrt{2}} \Rightarrow γ = \frac{π}{4} ∴ n = 4 \end{array}$

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