Question

Determine whether the vectors u and v are parallel, orthogonal, or neither.

u = <6, -2>, v = <8, 24>

a. Neither
b. Parallel
c. Orthogonal

Answer 1

Answer on Question #58210 – Math – Vector Calculus

Question

Determine whether the vectors $u$ and $v$ are parallel, orthogonal, or neither.

$$u = \langle 6, -2 \rangle, v = \langle 8, 24 \rangle$$

a. Neither

b. Parallel

c. Orthogonal

Solution

Vectors $u = \langle 6, -2 \rangle$ and $v = \langle 8, 24 \rangle$ are orthogonal, because their scalar (dot) product is equal to zero:

$$(u, v) = 6 \cdot 8 + (-2) \cdot 24 = 48 - 48 = 0.$$

Vectors $u = \langle 6, -2 \rangle$ and $v = \langle 8, 24 \rangle$ are not parallel, because their coordinates are not proportional:

$$\frac{6}{8} \neq \frac{-2}{24} \quad \text{(indeed, } \frac{3}{4} \neq \frac{-1}{12}).$$

Answer: c. Orthogonal.

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