To add vectors, you start from the beginning and draw a line to the end. This will create a triangle. By using Pythagorean Theorem, the length of the line can be obtained, which will be the scalar value of the vectors. To find the direction, trigonometry is used.
To calculate the angle of the vector, it would be 90-theta. To calculate theta, tan^-1 (vertical/horizontal) is used.
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