Q&A for How to Add or Subtract Vectors

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How can I find the resultant if angles are not given and only magnitudes are given?

Community Answer

If these are vectors, and you have no other information about their direction, you can't! Since you don't know the angles (or the relative alignment) between them, it's possible that the vectors could line up exactly (in which case the resultant has a magnitude equal to the sum of their magnitudes), or they could point in opposite directions (in which case the resultant has a magnitude equal to the difference between their magnitudes), or anywhere in between. If you were given a problem like this, it is not completely specified.

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Question

How do I add six or more than six vectors?

Community Answer

Adding n vectors is easy because vectors obey the superposition principle. Simply add their components.

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Question

I thought one of the processes in adding vectors is cross-multiplication?

Community Answer

The cross product is a type of multiplication, not addition, which pertains to this article.

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Question

To subtract a vector with the head to tail method, do I change only the first vector or both of them in an equation?

Community Answer

Just the second. You're using a-b = a + (-b) so that you can use the addition version of the head to tail method on a and (-b). Here, a is unchanged, and (-b) is the same vector as b except that its head and tail ends are swapped.

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Question

After changing the second vector direction, do I then add the two components or subtract them?

Community Answer

If you have reversed the second vector, you can now add the components of the first vector and the reversed second vector in order to get the difference. This is similar to how adding a negative number is the same as subtracting a positive version of that number, e.g. 2 - 1 = 2 + (-1) = 1.

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