Chapter 9, Problem 76RE

To determine

To calculate:A vector $v$ is in the form $v=ai+bj+ck$ ,where $v$ has initial point $P=\left(0,-4,3\right)$ and terminal point $Q=\left(6,-5,-1\right)$ .

Answer to Problem 76RE

Thevectorsis: $3i-5j+3k$ .

Explanation of Solution

Given information:

The initial point $P$ and terminalpoints $Q$ are given:

  $P=\left(0,-4,3\right)$ and $Q=\left(6,-5,-1\right)$ .

Formula used:

The formula to find the vector:

  $\overrightarrow{Q}-\overrightarrow{P}=\overrightarrow{PQ}$ .

Calculation:

Consider the initial and finalpoints:

  $P=\left(0,-4,3\right)$ and $Q=\left(6,-5,-1\right)$ .

Now write these points in the form of vectors:

  $\overrightarrow{P}=0i-4j+3k$ and $\overrightarrow{Q}=6i-5j-k$

To calculate vector $\overrightarrow{PQ}$ .

Subtract the vector $\overrightarrow{Q}-\overrightarrow{P}=\overrightarrow{PQ}$ .

Now apply the values in this: $\overrightarrow{Q}-\overrightarrow{P}=\overrightarrow{PQ}$ .

  $\begin{array}{l}\overrightarrow{PQ}=\overrightarrow{Q}-\overrightarrow{P}\\ \overrightarrow{PQ}=\left(6i-5j-k\right)-\left(0i-4j+3k\right)\\ \overrightarrow{PQ}=6i-5j+4j-k-3k\\ \overrightarrow{PQ}=6i-j-4k\end{array}$

Thus, The vector: $\overrightarrow{PQ}=6i-j-4k$ .