let v be the vector from the point (0, 4, 0) to the point (8, -6, 4), then v can be given in the component…

let v be the vector from the point (0, 4, 0) to the point (8, -6, 4), then v can be given in the component form as

let v be the vector from the point (0, 4, 0) to the point (8, -6, 4), then v can be given in the component form as

Answer

Explanation:

Step1: Recall vector - component formula

If a vector $\mathbf{v}$ goes from point $P(x_1,y_1,z_1)$ to point $Q(x_2,y_2,z_2)$, then $\mathbf{v}=\langle x_2 - x_1,y_2 - y_1,z_2 - z_1\rangle$.

Step2: Identify the coordinates

Here, $x_1 = 0,y_1 = 4,z_1 = 0$ and $x_2 = 8,y_2=-6,z_2 = 4$.

Step3: Calculate the components

$x_2 - x_1=8 - 0 = 8$, $y_2 - y_1=-6 - 4=-10$, $z_2 - z_1=4 - 0 = 4$. So, $\mathbf{v}=\langle8,-10,4\rangle$.

Answer:

$\langle8,-10,4\rangle$