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Find the component of a 50 N force which makes an angle of $45 °$ with z-axis and whose projection in XY-plane makes $45 °$ with the X-axis.

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$F_{x} = 25 N$

$F_{y} = 25 \sqrt{2} N$

$F_{y} = 25 N$

$F_{z} = 25 \sqrt{2} N$

answer is D.

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Detailed Solution

$α = 45 °; β = 90 °; γ = 45 ° F_{x} = F \cos α = 50 \times \frac{1}{\sqrt{2}} = \frac{50}{\sqrt{2}} = 25 \sqrt{2} F_{y} = F \cos β = 0 F_{x} = F \cos γ = 50 \times \frac{1}{\sqrt{2}} = 25 \sqrt{2} N$

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