Q&A for How to Resolve a Vector Into Components

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How do I find the magnitude and direction of a vector?

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The magnitude of the resultant vector can be found using either "the parallelogram law (or) the triangle law of vectors."

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What are the minimum components that we can use to resolve a vector into its components?

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The only component needed is the angle with which the vector meets with any one of the two axes.

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How do I resolve a vector into components without degrees?

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A vector can be resolved into components only if it makes some angle with either of the two axes(X/Y-axes).

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How can I find the perpendicular components of a force of 50N making an angle of 30° with an x-axis?

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(i) Y= (50N)sin30 = (50N) * 0.5 = 25N (ii) X= (50N)cos30 = (50) * 0.7 = 43.3N. The Y- axis represents the horizontal component while the X- axis represents the vertical component .

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Is it true that when a vector makes angle 90 degree to the horizontal, it can be resolved by taking cos 0 degree?

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The cosine function is used to calculate the horizontal magnitude of the vector. If your vector is 90 degrees to the horizontal, that means it is a straight vertical line, with no horizontal component. Then yes, the cosine will be 0.

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Question

What is the resolution of vector?

Community Answer

Resolution of vector is a process where one vector is broken down into two or more smaller vectors.

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What is the reasoning behind resolution of vectors?

Community Answer

For calculating the magnitude and direction of the resulting vector from two or more vectors.

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How do I resolve more than two vectors?

Community Answer

Just repeat the process. If you have, say five vectors operating together, you can add all five horizontal components together, and then add all five vertical components together. The two sums are the horizontal and vertical components, respectively, of the resultant vector.

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Is x-component always cos(angle) and y-component always sin(angle)?

Community Answer

In most cases, it is like that. The main reason is that the Y-component is supposed to be opposite the angle while the X-component is usually adjacent to the angle. It is the main reason we use the trigonometric method to ease up things.as we get use of SOHCAHTOA. Sin=opp/hypotenuse, Cos=adj/hypotenuse, Tan=opp/adjacent.

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What is the value of Fz in the resolution of a vector?

Community Answer

This cannot be answered without more data. I assume that by Fz, you mean the force in the "z" direction. This article focuses on 2-dimensional vectors, working only with the x and y axes. However, you can do exactly the same calculations in more than 2 dimensions. When you refer to the "z" axis, you are talking about a force in 3-dimensional space.

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