How would you add two vectors that are not perpendicular or parallel?

Question

How would you add two vectors that are not perpendicular or parallel?

Answer 1

Do they intersect? And what are their relative directions?

Answer 2

Just sum each component.  If vector 1 is <a, b, c> and vector 2 is <d, e, f>, when you add them you will get <a+d, b+e, c+f>.

Remember to keep any negative signs.  For a two-dimensional example, if you're adding <-2, 4> to <1, 3> you would get <-2+1, 4+3>, which is <-1, 7>.

Answer 3

The trick is to find the horizontal and vertical parts of each original vector.

You will then add the vertical parts together to form the vertical part of a super vector.  Add the horizontal parts of the original vectors to form the horizontal part of the super vector.  Using the added vertical parts and the added horizontal parts of the original vectors, you can then make that super vector which will be the correct resultant of the two original vectors.

The neat thing about this method is that it works for any number of original vectors. The hard part of this method is keeping track of all these values and only adding vertical to vertical and horizontal to horizontal. It is actually easier than it sounds.

Answer 4

Let one vector be 'p' and the other be 'q'. As you said that they are neither perpendicular not parallel, so let 'x' be the angle between them.

To add the vectors, we use the paralellogram law of vectors which says that the resultant vector

R = sqrt{p^2 + q^2 + 2pqcosx}

use this relation and a third vector will be obtained by you which will be the sum of p and q.