Find the vector PR given PQ = d and RQ = c in a vector diagram.

Question

ScanSolve AI Tutor · Accepted Answer

Here's the solution for question 9 (a) based on the provided vector diagram:

9. (a) Find the vector $\vec{PR}$ .

Identify the path from P to R using the given vectors.
From the diagram, we can express the vector $\vec{PR}$ as the sum of vectors $\vec{PQ}$ and $\vec{QR}$ .
$\vec{PR} = \vec{PQ} + \vec{QR}$
Substitute the given vector values.
We are given:
- $\vec{PQ} = \underline{d}$
- $\vec{RQ} = \underline{c}$
Determine $\vec{QR}$ from $\vec{RQ}$ .
The vector $\vec{QR}$ is the negative of $\vec{RQ}$ .
$\vec{QR} = -\vec{RQ} = -\underline{c}$
Substitute $\vec{PQ}$ and $\vec{QR}$ into the equation for $\vec{PR}$ .
$\vec{PR} = \underline{d} + (-\underline{c})$ $\vec{PR} = \underline{d} - \underline{c}$
The vector $\vec{PR}$ is $\boxed{\underline{d} - \underline{c}}$ .

Answer