Fractions and Decimals

Discrete Mathematics

Differential Equations

Solved on Nov 28, 2023

Find the vector $4\mathbf{v}$ given $\mathbf{v}=\langle-6,0\rangle$ .

STEP 1

Assumptions
1. The vector $\mathbf{v}$ is given as $\langle-6,0\rangle$ .
2. We are asked to calculate $4\mathbf{v}$ , which means we need to multiply the vector $\mathbf{v}$ by the scalar 4.

STEP 2

To multiply a vector by a scalar, we multiply each component of the vector by the scalar. The formula for scalar multiplication of a vector is:
$k\mathbf{v} = k\langle v_1, v_2 \rangle = \langle kv_1, kv_2 \rangle$
where $k$ is the scalar and $\mathbf{v}$ is the vector with components $v_1$ and $v_2$ .

STEP 3

Now, plug in the given values for the scalar and the vector into the formula.
$4\mathbf{v} = 4\langle-6,0\rangle = \langle 4(-6), 4(0) \rangle$

STEP 4

Perform the multiplication to get the resulting vector.
$4\mathbf{v} = \langle 4(-6), 4(0) \rangle = \langle -24, 0 \rangle$
So, $4\mathbf{v} = \langle -24, 0 \rangle$ .

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