Determine whether the vectors u and v are parallel, orthogonal, or neither.
u = < 8, 4>
v = < 10, 7> .

The vectors are neither parallel nor orthogonal.

Step-by-step explanation:

We are given the vectors as,

u = <8,4> and v = <10,7>

So, their dot product is given by,

u · v = <8,4> · <10,7> = 8×10 + 4×7 = 80 + 28 = 108 ≠ 0

As, we know, Two vectors are orthogonal if their dot product is 0.

Since, u · v = 108 ≠ 0

Thus, they are not orthogonal.

Also, Two vectors are parallel if angle between them is 0° or 180°.

So, we will find the angle between u and v.

As, ║u║ = = = = 8.94

As, ║v║ = = = = 12.2

So, we have,

i.e.

i.e.

i.e.

i.e.

Thus, θ ≈ 8.03°, which is not equal to 0° or 180°.

Then, the vectors are not parallel.

Hence, we see that the vectors are neither parallel nor orthogonal.

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