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.

x =±sqrt(1/3)

step-by-step explanation:

x+4/6x=1/x

multiply each side by 6x to get rid of the fractions

6x*(x+4/6x)=1/x*6x

distribute

6x^2 +4 = 6

subtract 4 from each side

6x^2 +4-4 = 6-4

6x^2 =2

divide by 6

6x^2/6 = 2/6

x^2 = 1/3

take the square root of each side

sqrt(x^2) = ±sqrt(1/3)

x =±sqrt(1/3)