Chapter 9.6, Problem 32AYU

In Problems 27-32, the vector $v$ has initial point $P$ and terminal point $Q$. Write $v$ in the form $ai+bj+ck$; that is, find its position vector.

$P=\left(-1,4,-2\right)$; $Q=\left(6,2,2\right)$

To determine

To find: The position vector of the vector $v$ which has the initial point $P$ and terminal point $Q$.

Answer to Problem 32AYU

Solution:

$7i - 2j + 4k$

Explanation of Solution

Given:

$P = (-1, 4, 2); Q = (6, 2, 2)$

Calculation:

The position vector of $v$ is $ai + bj + ck$ where $a, b, c$ are scalars and $i, j, k$ are unit vectors.

Then we get,

$\begin{array}{l}ai + bj + ck = (6 + 1)i + (2 - 4)j + (2 + 2)k\\ ai + bj + ck = 7i-2j + 4k\end{array}$