Question

Find the components of a 50N force which makes an angle of 45 with the z-axis whose projection on the xy plane is inclined 45 with the x-axis

Answer 1

Answer:This may help you

Explanation:

Answers are as follows as:-

1)50.sin(90+45)

50 cos(45)

50/root2

25.root2

2)50.cos(90+45)

-50.sin(45)

-25root2

Answer 2

Answer: The force (F)  can be broken down into components in x, y and z direction as F = 25 i + 25 j + 25√2 k

Explanation:

Any vector in 3d space can be broken into components using the magnitude of the vector (r), its angle made from the z-axis (θ) and the angle made by the projection of vector in xy-plane from the x-axis (Φ)

$z = rcos\theta$

$x = rsin\theta cos\phi$

$y = rsin\theta sin\phi$

Given :

r = 50 N

θ = 45°

Φ = 45°

z = 50cos(45)

$z = \frac{50}{\sqrt{2} } = 25\sqrt{2}$

x = 50sin(45)cos(45)

$x = \frac{50}{\sqrt{2}\sqrt{2} } = \frac{50}{2} = 25$

y = 50sin(45)sin(45)

$y = \frac{50}{\sqrt{2}\sqrt{2} } = \frac{50}{2} = 25$

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