How do you calculate the length of vector (0, 5)?

To calculate the length of vector (0, 5), use the Pythagorean theorem: √(0² + 5²) = 5.

In more detail, the length of a vector, also known as its magnitude, can be found using the Pythagorean theorem. For a vector given by its components (x, y), the formula to find its length is √(x² + y²). This formula comes from the Pythagorean theorem, which relates the sides of a right-angled triangle.

For the vector (0, 5), the x-component is 0 and the y-component is 5. Plugging these values into the formula, we get:

Length = √(0² + 5²)

First, square the components:
0² = 0
5² = 25

Next, add these squared values together:
0 + 25 = 25

Finally, take the square root of the sum:
√25 = 5

So, the length of the vector (0, 5) is 5. This makes sense because the vector points straight up along the y-axis, and its length is simply the distance from the origin (0, 0) to the point (0, 5), which is 5 units.