Compute the dot product v·w for v = ⟨1, -1, 2⟩ and w = ⟨-2, 0, 3⟩.

Compute the dot product v·w for v = ⟨1, -1, 2⟩ and w = ⟨-2, 0, 3⟩.

• A. -4
• B. 0
• C. 4
• D. 8

Answer: (C)

The dot product is found by multiplying corresponding components and summing the results. Multiply 1 by -2 to get -2, multiply -1 by 0 to get 0, and multiply 2 by 3 to get 6. Add them: -2 + 0 + 6 = 4. So v·w equals 4. A positive result means the vectors have some alignment in the same general direction (the angle between them is acute, since cos theta is positive). The other numbers don’t fit because the actual sum of the componentwise products is 4; you’d need different signs or magnitudes to obtain -4, 0, or 8.

The dot product is found by multiplying corresponding components and summing the results. Multiply 1 by -2 to get -2, multiply -1 by 0 to get 0, and multiply 2 by 3 to get 6. Add them: -2 + 0 + 6 = 4. So v·w equals 4. A positive result means the vectors have some alignment in the same general direction (the angle between them is acute, since cos theta is positive). The other numbers don’t fit because the actual sum of the componentwise products is 4; you’d need different signs or magnitudes to obtain -4, 0, or 8.