What is the scalar (dot) product of vectors u = 3i - 4j and v = 2i + 5j, and what is their angular relationship?
Answer and explanation
Correct answer: B. u . v = 14
- Step 1: Dot product formula: u . v = u_x v_x + u_y v_y = (3)(2) + (-4)(5) = 6 - 20 = -14. Step 2. Since u . v = |u||v|cos(theta) < 0, cos(theta) is negative, meaning the angle theta is obtuse (between 90 and 180 degrees). Answer: u . v = -14. Why not the others: A dot product of 0 indicates perpendicularity; positive indicates acute.
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