Given vectors u = <3, -1, 4> and v = <2, 5, -1> in 3D space, what is their dot (scalar) product u . v?
Answer and explanation
Correct answer: C. -3
- Step 1: The dot product of two vectors <u1, u2, u3> and <v1, v2, v3> is: u . v = u1v1 + u2v2 + u3*v3.
- Step 2: Compute each component product: (3)(2) + (-1)(5) + (4)(-1).
- Step 3: Calculate: 6 - 5 - 4 = -3.
Answer
-3.
Why not the others: '5' calculates 6 - 5 + 4 by missing the negative sign on v3; '15' sums the absolute values; '-7' makes an arithmetic error during subtraction.
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