How do you determine whether u and v are orthogonal, parallel or neither given #u=<3, 15># and #v=<-1, 5>#?

2 Answers
Dec 13, 2016

Answer:

Please see the explanation.

Explanation:

Compute the dot-product:

#baru*barv = 3(-1) + 15(5) = 72#

The two vectors are not orthogonal; we know this, because orthogonal vectors have a dot-product that is equal to zero.

Determine whether the two vectors are parallel by finding the angle between them.

Compute the magnitude of both vectors:

#||baru|| = sqrt(3^2 + 15^2) = sqrt(234)#

#||barv|| = sqrt((-1)^2 + 5^2) = sqrt(26)#

The angle between them is:

#theta = cos^-1(72/(sqrt(234)sqrt(26)))#

#theta ~~ 22.6^@#

If they were parallel the angle would be #0^@ or 180^@#, therefore, the two vectors are not parallel.

The answer is neither.

Dec 13, 2016

Answer:

The vectors are not parallel and not orthogonal.

Explanation:

To see if 2 vectors, we do a dot product

#vecu.vecv=〈3,15〉.〈-1,5〉=3*-1+15*5=-3+75=72#

As the dot product is #!=0#, the vectors are not perpendicular

If 2 vectors are parallel,

then, #vecu=kvecv#

#〈3,15〉=k〈-1,5〉#

#3=-k# and #15=5k#

Therefore, #k=-3# and #k=3#

This is not possible, so the vectors are not parallel