Let A represent any nonzero vector. Why is$\raisebox{1ex}{$\overrightarrow{A}$}\!\left/ \!\raisebox{-1ex}{$A$}\right.$a unit vector, and what is its direction? If$\theta$ is the angle that Amakes with the +x-axis, explain why$\raisebox{1ex}{$\overrightarrow{A}$}\!\left/ \!\raisebox{-1ex}{$A$}\right.$ is called the direction cosinefor that axis.

The vector's various coordinates are presented here.

A vector having themagnitude of 1and no units is called a unit vector. Its sole function is to point, or to describe a spatial direction.

For many formulas involving vector components, unit vectors are a useful notation.

A unit vector dn pointing in the positive x-axis and a unit vector en pointing in the positive y-axis can be defined in a xy-coordinate system.

We know that in coordinates, the x component of a vector comes first, followed by the y component.

To calculate the angle of the vector with respect to the x axis, just multiply the y component by the x component and then take the inverse of that result.

This will tell you thevector's angle with the x axis.

To determine: The justification behind the unit vector's name, as well as its direction.

The x-axis was given the moniker direction cosine for a purpose.

As its magnitude is 1 and its direction is the same as the vector, the quantity is called aunit vector.

Because it equals the angle formed by the vectors with the positive x-axis, the quantity is called direction cosine for x-axis.

The quantity has a magnitude of one. As a result, it is referred to as a unit vector. Calculate the quantity's value.

The vector's angle with the positive x-axis is Cosine direction. As a result, the quantity is known as x-axis direction cosine.