How do you express a vector in unit vector notation?

A vector is expressed in unit vector notation by breaking it down into its component parts along the x, y, and z axes.

In more detail, a vector is a quantity that has both magnitude (size) and direction. In physics, we often deal with vectors in three dimensions, so we need a way to express these vectors in a standardised way. This is where unit vector notation comes in.

Unit vectors are vectors of length 1 that point in the direction of the positive x, y, and z axes. They are usually denoted by the letters i, j, and k respectively. For example, i is a unit vector in the direction of the positive x-axis, j is a unit vector in the direction of the positive y-axis, and k is a unit vector in the direction of the positive z-axis.

To express a vector in unit vector notation, you need to break it down into its components along the x, y, and z axes. This is done by projecting the vector onto each axis. The magnitude of the projection onto each axis is the component of the vector along that axis.

For example, let's say we have a vector A that has components of 3 along the x-axis, -2 along the y-axis, and 1 along the z-axis. In unit vector notation, this would be written as 3i - 2j + k. The coefficients of i, j, and k (3, -2, and 1 in this case) are the components of the vector along the x, y, and z axes respectively.

Remember, the sign of the component indicates the direction along that axis. A positive component means the vector is pointing in the direction of the positive axis, while a negative component means it's pointing in the direction of the negative axis.

In summary, expressing a vector in unit vector notation involves breaking it down into its components along the x, y, and z axes, and then writing it as the sum of these components times the corresponding unit vectors.