This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.

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Answer
B. \vec{PR} = \begin{pmatrix} 5 \ -6 \end{pmatrix}
Step 1: Identify the given vectors. We are given the vectors and :
Step 2: Use the triangle law of vector addition to find . The vector can be found by adding the vectors and :
Step 3: Substitute the given vectors and perform the addition. Add the corresponding components:
Step 4: Compare the result with the given options. The calculated vector matches option B.
The final answer is .
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Identify the given vectors. We are given the vectors PQ and QR: PQ = -3 \\ -4 QR = 8 \\ -2 Step 2: Use the triangle law of vector addition to find PR.
This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.