A ship travels from port P to port Q. The displacement vector is $\vec{PQ} = \begin{pmatrix} 12 \ -5 \end{pmatrix}$ km. What is the magnitude of $\vec{PQ}$?

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Question

A ship travels from port P to port Q. The displacement vector is $\vec{PQ} = \begin{pmatrix} 12 \ -5 \end{pmatrix}$ km. What is the magnitude of $\vec{PQ}$?

Accepted Answer

13 km — Award 1 mark for correct use of Pythagoras: |PQ| = √(12² + (−5)²) = √(144 + 25) = √169 = 13 km. A is incorrect — this is 12 − 5, a common error of subtracting components. C is incorrect — this is 12 + 5, adding components instead of using Pythagoras. D is incorrect — this is 12² + 5² without taking the square root.

Answer

13 km

Answer

169 km

Answer

7 km

Answer

17 km

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