# Let v = -9i + 3j. Find the vector 2v.

## Question:

Let {eq}\displaystyle\; \mathbf{v} = -9\mathbf{i} + 3\mathbf{j} {/eq}.

Find the vector {eq}\displaystyle\; 2\mathbf{v} {/eq}.

## Scalar Multiplication of Vectors:

A vector is defined as a quantity that has both the magnitude and the direction. The scalar multiplication of vectors involves the multiplication of a vector by a scalar or a constant. For example, if we have a two-dimensional vector {eq}z = x + iy {/eq} multiplied by a constant {eq}k {/eq}, then we form a new vector {eq}z_1 = kx + iky {/eq}.

We have a two-dimensional vector:

• {eq}v = -9i + 3j {/eq}

Therefore, {eq}2v {/eq} will be equal to:

• {eq}2v =2 (-9i + 3j) {/eq}
• {eq}\boxed{\color{blue}{2v = -18i + 6j}} {/eq}