Question

If u = ❬6, –9❭ and v = ❬–24, 36❭ with an angle θ between the vectors, are u and v parallel or orthogonal? Explain.
The vectors are parallel because cos θ = −1.
The vectors are parallel because u • v = 0.
The vectors are orthogonal because u • v = 0.
The vectors are orthogonal because cos θ = −1.

Answer 1

@jhonyy9 could you help me out dawg?

Answer 2

1. Use the dot product
2. Find the magnitude of both vectors

The formula is arccos((v dot u)/(||v||*||u||)

Answer 3

so could you walk me through it @sherixn

Answer 4

Sure! So first find u dot v

which is defined as u * v = (u1)(v1) + (u2)(v2)

Answer 5

which would be 6(-24) + -9(36)

Answer 6

This equals -468

The magnitude formula is ||v|| = \[\sqrt{a^2+b^2}\]

Same for ||u||= \[\sqrt{a^2+b^2}\]

Answer 7

||v|| = sqrt[6^2+(-9)^2]
||u|| = sqrt[(-24)^2+36^2]

Answer 8

||v||=sqrt(117)
||u||= 4sqrt(117)

Answer 9

Now we take the inverse cosine of -468/sqrt(117)*4sqrt(117)

Answer 10

This equals 180

Answer 11

When the angle is 180, cos = -1 (you can look at the unit circle of reference)

Answer 12

So the answer is A. "The vectors are parallel because cos θ = −1."

Answer 13

thank you, sorry for the late reply i was busy @sherixn

Answer 14

No problem, I figured @pacman25 (: