Answer:
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║ = \(\sqrt{8^{2}+4^{2}}\) = \(\sqrt{64+16}\) = \(\sqrt{80}\) = 8.94
As, ║v║ = \(\sqrt{10^{2}+7^{2}}\) = \(\sqrt{100+49}\) = \(\sqrt{149}\) = 12.2
So, we have,
\(\theta = \cos^{-1} \frac{u\cdot v}{\left \| u \right \|\times \left \| v \right \|}\)
i.e. \(\theta = \cos^{-1} \frac{108}{8.94\times 12.2|}\)
i.e. \(\theta = \cos^{-1} \frac{108}{109.068}\)
i.e. \(\theta = \cos^{-1} 0.9902\)
i.e. \(\theta = 8.03\)
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.
