graph $-3\\mathbf{w}$ with its initial point at the initial point of $\\mathbf{w}$.
graph $-3\\mathbf{w}$ with its initial point at the initial point of $\\mathbf{w}$.
Answer
Explanation:
Step1: Identify the components of vector $\mathbf{w}$
The initial point of $\mathbf{w}$ is $(2, 6)$ and the terminal point is $(6, 10)$. $$ \mathbf{w} = \langle 6 - 2, 10 - 6 \rangle = \langle 4, 4 \rangle $$
Step2: Calculate the components of $-3\mathbf{w}$
Multiply each component of $\mathbf{w}$ by the scalar $-3$. $$ -3\mathbf{w} = -3 \langle 4, 4 \rangle = \langle -12, -12 \rangle $$
Step3: Determine the terminal point of $-3\mathbf{w}$
The initial point is $(2, 6)$. Add the vector components to the initial point. $$ (x, y) = (2 + (-12), 6 + (-12)) = (-10, -6) $$
Answer:
To graph $-3\mathbf{w}$, draw a vector starting at the initial point $(2, 6)$ and ending at the terminal point $(-10, -6)$.