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nexus9112 [7]
2 years ago
15

State if the two vectors are parallel, orthogonal, or neither. u=18i+8j v=9i+4j

Mathematics
1 answer:
Iteru [2.4K]2 years ago
8 0

Answer:

Parallel, since \vec u = 2\cdot \vec v.

Step-by-step explanation:

The relation between both vectors is determined by the use of the dot product, whose expression is:

\cos \theta = \frac{\vec u \bullet \vec v}{\|\vec u\| \|\vec v\|}

Where:

\cos \theta = 1 if vectors are parallel to each other and \cos \theta = 0 if vectors are orthogonal. Then, norms and dot product are calculated hereafter:

\|\vec u\| = \sqrt{18^{2}+8^{2}}

\|\vec u\| \approx 19.698

\|\vec v \| = \sqrt{9^{2}+4^{2}}

\|\vec v\| \approx 9.849

\vec u \bullet \vec v = (18)\cdot (9) + (8)\cdot (4)

\vec u \bullet \vec v = 194

\cos \theta = \frac{194}{(19.698)\cdot (9.849)}

\cos \theta = 1

The two vectors are parallel to each other, which is also supported by the fact that one vector is multiply of the other one. That is,

18i + 8j = 2\cdot (9i + 4j)

\vec u = 2\cdot \vec v

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