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## Precalculus

### Course: Precalculus>Unit 6

Lesson 8: Adding vectors in magnitude and direction form

# Adding vectors in magnitude and direction form

In this example, Sal takes two vectors given by magnitude and direction, and finds the magnitude and direction of their sum. Created by Sal Khan.

## Want to join the conversation?

• Is there no formula to do this more easily?
• Sal incorporated the equation into the problem. If you have a vector with magnitude |a| and at an angle α from positive x axis and a vector with magnitude of |b| at an angle of ß from the positive x axis,
the x coordinate of the vector sum is |a|cos(α)+|b|cos(ß) and the y coordinate is |a|sin(α)+|b|sin(ß).
• when finding the direction why cant we just use 170+240/2
• When finding the direction of the resulting vector, we can't simply take the average of the angles of vector a and vector b. This is because the direction of the resulting vector is influenced not only by the individual directions of vector a and vector b, but also by the relative magnitudes of the two vectors.

To find the direction of the resulting vector, we need to use trigonometry. We can use the inverse tangent function to find the angle whose tangent is the ratio of the y-component to the x-component of the resulting vector. We can then adjust the angle as necessary based on the quadrant in which the resulting vector lies.
• To get the coordinates of a vector (x,y), do we always use cos for X and sin for Y? Or does it depend on which quadrant it is. Sorry if this may seem out of order
(1 vote)
• Assuming the angle is measured from the x axis, then yes, cosine always comes with the x coordinate and sine with the y. However, it's always better to derive the components from scratch and not assume this is always the case, as if the angle is measured from the y axis, this gets reversed (the y coordinate associates with cosine and the x coordinate associates with sine)