What is the unit vector in the direction of (5, 0)?

The unit vector in the direction of (5, 0) is (1, 0).

To understand this, let's first recall what a unit vector is. A unit vector is a vector that has a magnitude (length) of exactly 1. It is used to indicate direction without considering the magnitude of the original vector. To find the unit vector in the direction of a given vector, we need to divide each component of the vector by its magnitude.

The given vector is (5, 0). To find its magnitude, we use the formula for the magnitude of a vector, which is the square root of the sum of the squares of its components. For the vector (5, 0), the magnitude is calculated as follows:

\[ \text{Magnitude} = \sqrt{5^2 + 0^2} = \sqrt{25} = 5 \]

Next, we divide each component of the vector (5, 0) by this magnitude. This gives us:

\[ \text{Unit vector} = \left( \frac{5}{5}, \frac{0}{5} \right) = (1, 0) \]

So, the unit vector in the direction of (5, 0) is (1, 0). This means that the direction of the vector (5, 0) is purely along the x-axis, and the unit vector (1, 0) represents this direction with a magnitude of 1. This concept is very useful in various applications, such as physics and engineering, where direction is important but the actual magnitude can be normalised to 1 for simplicity.