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Q.

If a vector $\vec{A}$ makes angles $45 °$ and $60 °$ with $x$ and $y$ axis respectively then the angle made by it with $z$ - axis is

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a

$60 °$

b

$120 °$

c

$30 °$

d

$90 °$

answer is B.

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Detailed Solution

$α = 45^{\circ}; β = 60^{\circ}; γ = ?$

$\cos^{2} α + \cos^{2} β + \cos^{2} γ = 1$

$\Rightarrow \cos^{2} γ = 1 - \frac{3}{4} = \frac{1}{4}$

$\cos γ = \pm \frac{1}{2} \Rightarrow γ = 60^{\circ} (or) 120^{\circ}$

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If a vector A→ makes angles 45° and 60° with x and y axis respectively then the angle made by it with z - axis is