Question

The two unit vectors perpendicular to the axis

Answer 1

What is the magnitude of the resultant of two unit vectors which are added when they are perpendicular to each other?

The answer is the square root of 2, which equals approximately 1.414.

You can think of the two perpendicular vectors as the perpendicular sides of a right triangle. The vector formed by adding them together is the third side - the hypotenuse.

The pythagorean equation is, c^2 = a^2 + b^2, where “a” and “b” are the lengths of the perpedicular sides, and ”c” is the hypotenuse.

So since our perpendicular vectors are also unit vectors, we know that both of their lengths (magnitudes) are 1 unit. We can plug those 1s into the pythagorean equation, and solve for the length of the hypotenuse, which is “c” in the equation, and also the magnitude of our summed vector.

c^2 = 1^2 + 1^2

One times one is still one, so simplifying the 1^2s:

c^2 = 1 + 1

Adding the numbers together:

c^2 = 2

Taking the square root of both sides:

c = sqrt(2)