Find a vector v for a vector equation $\mathbf { r } = \mathbf { r } _ { 0 } + t \mathbf { v }$ of the line passing through the points (1, 2, 3) and (4, 5, 6).
A) $\{ 1,1,0 \}$
B) $\{ 0,1,1 \}$
C) $\{ 1,0,1 \}$
D) $\{ 1,1,1 \}$
E) $\{ 0,0,1 \}$
F) $\{ 1,0,0 \}$
G) $\{ 0,1,0 \}$
H) $\{ 0,0,0 \}$

Question

Find a vector v for a vector equation $\mathbf { r } = \mathbf { r } _ { 0 } + t \mathbf { v }$ of the line passing through the points (1, 2, 3) and (4, 5, 6).
A) $\{ 1,1,0 \}$ 
B) $\{ 0,1,1 \}$ 
C) $\{ 1,0,1 \}$ 
D) $\{ 1,1,1 \}$ 
E) $\{ 0,0,1 \}$ 
F) $\{ 1,0,0 \}$ 
G) $\{ 0,1,0 \}$ 
H) $\{ 0,0,0 \}$

Quizplus · Accepted Answer

The vector $\mathbf{v}$ is found by subtracting the coordinates of the first point from the second point: $(4-1, 5-2, 6-3) = (3, 3, 3)$. To get a direction vector, we can scale this by $\frac{1}{3}$, resulting in $\{1, 1, 1\}$.

Find a Vector V for a Vector Equation r=r0+tv\mathbf { r } = \mathbf { r } _ { 0 } + t \mathbf { v }r=r0​+tv

Find a Vector V for a Vector Equation $\mathbf { r } = \mathbf { r } _ { 0 } + t \mathbf { v }$