Let w be a vector with initial point (4, -4) and terminal point (2, 5).Write w as a linear combination of the standard unit vectors i and j.
A) $\mathbf { w } = 8 \mathbf { i } - 3 \mathbf { j }$
B) $\mathbf { w } = 0 \mathbf { i } + 3 \mathbf { j }$
C) $\mathbf { w } = \mathbf { i } + 6 \mathbf { j }$
D) $\mathbf { w } = - 2 \mathbf { i } + 9 \mathbf { j }$
E) $\mathbf { w } = 6 \mathbf { i } - 9 \mathbf { j }$

Question

Let w be a vector with initial point (4, -4) and terminal point (2, 5).Write w as a linear combination of the standard unit vectors i and j.
A)  $\mathbf { w } = 8 \mathbf { i } - 3 \mathbf { j }$
B)  $\mathbf { w } = 0 \mathbf { i } + 3 \mathbf { j }$
C)  $\mathbf { w } = \mathbf { i } + 6 \mathbf { j }$
D)  $\mathbf { w } = - 2 \mathbf { i } + 9 \mathbf { j }$
E)  $\mathbf { w } = 6 \mathbf { i } - 9 \mathbf { j }$

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 from the terminal point: $(2 - 4, 5 - (-4)) = (-2, 9)$. Thus, $\mathbf{w} = -2\mathbf{i} + 9\mathbf{j}$.

Let W Be a Vector with Initial Point (4, -4) w=8i−3j\mathbf { w } = 8 \mathbf { i } - 3 \mathbf { j }w=8i−3j

Let W Be a Vector with Initial Point (4, -4) $\mathbf { w } = 8 \mathbf { i } - 3 \mathbf { j }$