Question

find \\(\vec{u} - \vec{v}\\), given that \\(\vec{u} = \langle -1, 4, 7 \
angle\\) and \\(\vec{v} = 3\mathbf{i} - 4\mathbf{j} + \mathbf{k}\\) your final answer should be written in component form. select one: a. \\(\langle 2, 0, 6 \
angle\\) b. \\(\langle -4, 8, 6 \
angle\\) c. \\(\langle -4, 0, 8 \
angle\\) d. \\(-4\mathbf{i} + 8\mathbf{j} + 6\mathbf{k}\\)

Explanation:

Step1: Convert $\vec{v}$ to component form

Given $\vec{v} = 3\boldsymbol{i} - 4\boldsymbol{j} + \boldsymbol{k}$, in component form, this is $\langle 3, -4, 1
angle$ (since the coefficient of $\boldsymbol{i}$ is the $x$-component, $\boldsymbol{j}$ is the $y$-component, and $\boldsymbol{k}$ is the $z$-component).

Step2: Subtract the components of $\vec{v}$ from $\vec{u}$

We know $\vec{u} = \langle -1, 4, 7
angle$ and $\vec{v} = \langle 3, -4, 1
angle$. To find $\vec{u} - \vec{v}$, we subtract the corresponding components:

• For the $x$-component: $-1 - 3 = -4$
• For the $y$-component: $4 - (-4) = 4 + 4 = 8$
• For the $z$-component: $7 - 1 = 6$

So, $\vec{u} - \vec{v} = \langle -4, 8, 6
angle$.

Answer:

b. $\langle -4, 8, 6
angle$