Question

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☘Form a vector F =25 N which is in the. direction of point 3 , 4 ?​☆



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Answer 1

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To find resultant of forces in 3D,

We can use R = √(Fx^2+Fy^2+Fz^2)

R = √(4500^2+2250^2+1100^2)

R = √(20250000+5062500+1210000)

R = √(26522500)

R= 5150 N.

Now since Resultant is a 3D vector, you will not get one angle theta as in case of 2D vectors.

So here you will get three angles (α,β,γ) between the resultant and the three axes (X ,Y,Z).

Let us say:

α is the angle between R and the x-axis (in dark red),

β is the angle between R and the y-axis (in green) and

γ is the angle between R and the z-axis (in pink)

So to find these angles,

Cos α = Fx/R= 4500/5150

=> α = 29.09°

Cos β = Fy/R = 2250/5150

=> β = 64.09°

Cos γ = Fz/R = 1100/5150

=> γ = 77.66°.

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Answer 2

Answer!

To find resultant of forces in 3D,

We can use R = √(Fx^2+Fy^2+Fz^2)

R = √(4500^2+2250^2+1100^2)

R = √(20250000+5062500+1210000)

R = √(26522500)

R= 5150 N.

Now since Resultant is a 3D vector, you will not get one angle theta as in case of 2D vectors.

So here you will get three angles (α,β,γ) between the resultant and the three axes (X ,Y,Z).

Let us say:

α is the angle between R and the x-axis (in dark red),

β is the angle between R and the y-axis (in green) and

γ is the angle between R and the z-axis (in pink)

So to find these angles,

Cos α = Fx/R= 4500/5150

=> α = 29.09°

Cos β = Fy/R = 2250/5150

=> β = 64.09°

Cos γ = Fz/R = 1100/5150

=> γ = 77.66°.

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