# Let u = 5i - j, v = 3i + j, w = i + 2j. Find the specified scalar. (4u) + v

## Question:

Let {eq}\displaystyle\quad \mathbf{u} = 5\mathbf{i} - \mathbf{j},\quad \mathbf{v} = 3\mathbf{i} + \mathbf{j},\quad \mathbf{w} = \mathbf{i} + 2\mathbf{j} {/eq}.

Find the specified scalar.

{eq}\displaystyle\; (4\mathbf{u}) + \mathbf{v} {/eq}

## Components of a Vector

A vector is a quantity with a magnitude and direction. In the cartesian coordinate system, vectors are conventionally represented by a line with an arrow. It can also be represented by its components in the x, y and/or z axes. These components are simply the projection of a vector in each of the said axes.

Correction: The result of the given expression is still a vector.

Given:

{eq}u = 5i - j\\[0.2cm] v = 3i + j\\[0.2cm] w = i + 2 {/eq}

When adding and subtracting vectors, we only combine the terms of the same direction. Thus, {eq}4(u)+v {/eq} is equivalent to

{eq}4(u)+v=4(5i - j)+ (3i + j)\\[0.2cm] 4(u)+v=20i - 4j+ 3i + j\\[0.2cm] \color{red}{4(u)+v=23i - 3j}\\[0.2cm] {/eq}