Let $\mathbf { w }$ be a vector with initial point $( 2,1 )$ and terminal point $( 9 , - 3 )$. Write $\mathbf { w }$ as a linear combination of the standard unit vectors $\mathbf { i }$ and $\mathbf { j }$.
A) $\mathbf { w } = \mathbf { i } + 12 \mathbf { j }$
B) $\mathbf { w } = - 5 \mathbf { i } + 8 \mathbf { j }$
C) $\mathbf { w } = 7 \mathbf { i } - 4 \mathbf { j }$
D) $\mathbf { w } = 11 \mathbf { i } + 4 \mathbf { j }$
E) $\mathbf { w } = 3 \mathbf { i } - 12 \mathbf { j }$

Question

Quizplus · Accepted Answer

To find the vector $\mathbf { w }$ as a linear combination of the standard unit vectors $\mathbf { i }$ and $\mathbf { j }$, subtract the initial point coordinates from the terminal point coordinates: $9 - 2 = 7$ for $\mathbf { i }$ and $-3 - 1 = -4$ for $\mathbf { j }$, resulting in $\mathbf { w } = 7 \mathbf { i } - 4 \mathbf { j }$.

Let w\mathbf { w }w Be a Vector with Initial Point (2,1)( 2,1 )(2,1)

Let $\mathbf { w }$ Be a Vector with Initial Point $( 2,1 )$