How do you add perpendicular vectors?

You add perpendicular vectors by using the Pythagorean theorem, which states that the magnitude of the resultant vector is the square root of the sum of the squares of the magnitudes of the individual vectors.

In more detail, when you have two vectors that are perpendicular to each other, you can't simply add their magnitudes together to get the magnitude of the resultant vector. This is because they are not pointing in the same direction. Instead, you have to use the Pythagorean theorem, which is a mathematical principle that applies to right-angled triangles.

The Pythagorean theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. In the context of vectors, the hypotenuse of the triangle is the resultant vector, and the other two sides are the individual vectors you are adding together.

To apply the Pythagorean theorem to vectors, you first square the magnitudes of the individual vectors, then add these squares together. The magnitude of the resultant vector is then the square root of this sum. This gives you the magnitude of the resultant vector.

To find the direction of the resultant vector, you can use trigonometric functions. The tangent of the angle that the resultant vector makes with one of the individual vectors is equal to the magnitude of the other vector divided by the magnitude of the first vector. You can then use the arctangent function to find the angle.

Remember, this method only works for vectors that are perpendicular to each other. If the vectors are not perpendicular, you will need to use a different method to find the resultant vector.