If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

### 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?

• 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.
• How come Sal can do the sins and cosines of angles greater than 90 degrees? For 4cos170, shouldn't it be 4cos10? or something?
• There is no difference, but 4cos170 is more direct because you will get the answer in negative, so fewer steps less wasted time in the exam.
• For all those who struggle this is actually very easy, just go back and do your trigonometry homework properly, here is a full course on that, finish that and came back to this.
• 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)
• how does Sal know its in the 3rd quadrant?
(1 vote)
• Sal knows that the vector is in the third quadrant because its x-component is negative and its y-component is negative. In general, when a vector is in the third quadrant, both its x and y components are negative.
• How do you find the other angles in the parallelogram made by the addition of these two vectors? For example, the angle made when he draws b onto the end of a at . Can you use the starting angles in some kind of formula? Thanks
(1 vote)
• Cant wait to graduate and forget all this
(1 vote)