Q. 13

Question

If the initial point of the vector $\langle2, 3, −5\rangle$ is the point $\left(-3, 2, 4\right)$, what is the terminal point of the vector?

Step-by-Step Solution

Verified

Answer

The terminal point of the vector is $\langle-5,-1,9\rangle$.

1Step 1. Given Information

The vector $v=\langle2,3,-5\rangle$ and the terminal point of the vector is $\left(-3,2,4\right)$.

2Step 2. The initial point of vector

If $v$ is the vector such that $P\left(x_{0},y_{0},z_{0}\right)$ is the initial point and $Q\left(x_{1},y_{1},z_{1}\right)$ is the terminal point, then vector $\overline{PQ}$is given by $\overline{PQ}=\langle x_{1}-x_{0},y_{1}-y_{0},z_{1}-z_{0}\rangle$.

Now, the terminal point is (Q\left(-3,2,4\right)\) Let the terminal point be $P\left(x,y,z\right)$

Therefore,

$\langle2,3,-5\rangle=\langle-3-x,2-y,4-z\rangle$

Comparing both sides,

$-3-x=2$

$2-y=3$

$4-z=-5$

Solve for $x, y, z$

$x=-3-2$

$x=-5$

$y=2-3$

$y=-1$