Let u = (3, -2, 5) and v = (1, 0, -4). What is the dot product u · v?

Let u = (3, -2, 5) and v = (1, 0, -4). What is the dot product u · v?

• A. -17
• B. 17
• C. -11
• D. 0

Answer: (A)

The dot product is found by multiplying corresponding components and adding those products. For u = (3, -2, 5) and v = (1, 0, -4), that’s 3·1 + (-2)·0 + 5·(-4) = 3 + 0 - 20 = -17. So the dot product is -17. The middle term vanishes because the second component of v is zero. The last product is negative since 5 and -4 have opposite signs, and the first product is positive, but not large enough to overcome the negative last term, giving a negative total. A negative dot product also tells you the vectors form an obtuse angle with each other.

The dot product is found by multiplying corresponding components and adding those products. For u = (3, -2, 5) and v = (1, 0, -4), that’s 3·1 + (-2)·0 + 5·(-4) = 3 + 0 - 20 = -17. So the dot product is -17.

The middle term vanishes because the second component of v is zero. The last product is negative since 5 and -4 have opposite signs, and the first product is positive, but not large enough to overcome the negative last term, giving a negative total. A negative dot product also tells you the vectors form an obtuse angle with each other.