QQuestionMathematics
QuestionMathematics
Given that a vector is the directed line segment from P(0,0) to Q(3,2), what is the magnitude of that vector?
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Answer
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Step 1:I'll solve this step-by-step using the vector magnitude formula:
Step 2:: Identify the Vector Coordinates
- Vector components: $$\vec{v} = \langle 3-0, 2-0 \rangle = \langle 3, 2 \rangle
- Ending point Q: (3,2)
Step 3:: Recall the Vector Magnitude Formula
|\vec{v}| = \sqrt{(x_{2}-x_{1})^{2} + (y_{2}-y_{1})^{2}}
The magnitude of a vector is calculated using the Pythagorean theorem:
Step 4:: Calculate the Magnitude
|\vec{v}| = \sqrt{13}
|\vec{v}| = \sqrt{9 + 4}
Final Answer
The magnitude of the vector is \sqrt{13} units.
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