Given 2D vectors u = 3i - 4j and v = -2i + 7j, find the magnitude of the resultant vector w = u + v.
Answer and explanation
Correct answer: D. √10 units
- Step 1: Add components: w = (3 - 2)i + (-4 + 7)j = 1i + 3j. Step 2. Magnitude formula: |w| = √(x² + y²) = √(1² + 3²) = √(1 + 9) = √10 units. Answer: √10 units. Why not the others: 5 units is |u|; √26 units results from incorrect component arithmetic; 4 units is 1 + 3.
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