CODEWITHSUNDEEP
mathtrigonometry
Tessa
Tessa

Reputation: 317

How to calculate a vector from an angle with another vector in 2D?

I know I should know this, but I just can't figure it out/find the solution. I can do it by hand, but I can't put it in an algorithm... (working in c++, but pseudocode should be fine).

I have a vector, and I want to find another vector based on the angle with it.

Angle with two vectors

v is known, angle alpha is known and the magnitude of w is known. How can I find w?

Thanks!

Upvotes: 12

Views: 17972

Answers (2)

Simon Nickerson
Simon Nickerson

Reputation: 43159

To rotate a vector v = (x, y) by an angle alpha clockwise about the origin, you can multiply by the matrix:

[  cos alpha    sin alpha ]
[ -sin alpha    cos alpha ]

Thus the rotated vector with the same magnitude will be

(x cos alpha + y sin alpha, -x sin alpha + y cos alpha).

To change the magnitude from |v| to |w|, multiply both co-ordinates by |w|/|v|.

Upvotes: 20

Phebus40
Phebus40

Reputation: 173

vector(w) = vector(v) / cos (alpha) to find the direction of w. You must multiply by magnitude(w)/magnitude(v) to set the magnitude

Upvotes: -2

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