How to add vectors

Vectors pointing in the same direction

These are the easiest kind of vectors to add. You can just pretend the directions aren't there and add the numbers. For example if you have to add 17m, East, and 13m East, just add the numbers and slap the direction on to the end. 30m, East is the correct answer. Another Example: 5m/s, 30° North of East + 2m/s, 30° North of East=7m/s, 30° North of East. It's pretty simple.

Vectors in the opposite direction

This one is a little trickier. What do you do when you have to add 10m, North and 30m, South? Step one: Find the larger number, in this case 30. Now subtract the smaller number from that. 30 - 10=20. Now just attach the direction from the larger number. 20m, South is the answer. It's just like adding negative numbers in math. Here is another example. 700N, 0° North of East + 300N, 0° North of West=400N, 0° North of East. As a side note, if you are asked to add many vectors, (I.e.: 1m, East + 2m, East + 3m, West + 4m, West) First add all the vectors pointing in the same direction (so you are left with 3m, East + 7m, West) then follow the steps above. (Final result equals 4m, West).

Adding perpendicular vectors

Now that we can add vectors on the same line, it's time to move onto the next section. Perpendicular Vectors. Your teacher asks you to add 300m, 0° North of East and 400m 90° North of East. Here's how you do it. Remember Geometry? Remember the Pythagorean theorem? (a² + b² =c²) We have to use that. Since the vectors are at right angles to each other, we can form a right triangle out of them. The resultant vector (the answer) will be the third side of the triangle. Use the vectors you have as the bases of the triangle and plug it into the equation.

a² + b² =c²
300m² + 400m²=c²
250000m²=c²
c=500m

We still need to find the exact angle that the vector points. To do that we need to sell our soul to the demon of trigonometry. If you remember Tan=Opposite side/adjacent side. So, Tan=400m/300m, Tan=1.3333, Inverse Tan=53°. So the final answer is 500m, 53° North of East.