Question

How do you determine whether u and v are orthogonal, parallel or neither given `u=1/4(3i-j)` and `v=5i+6j`?

Answer 1

THe vectors are neither ortogonal nor parallel

Explanation:

The vectors are
`vecu=〈3/4,-1/4〉`
`vecv=〈5,6〉`
For 2 vectors to be ortogonal, the dot product is `=0`
Here, `vecu.vecv=〈3/4,-1/4〉.〈5,6〉=15/4-6/4=9/4!=0`

Therefore, `vecu` and `vecv` are not ortogonal.

For `2` vectors to be parallel, `vecu=kvecv` where k is a scalar.
`〈3/4,-1/4〉=k〈5,6〉`
So, `3/4=5k` `=>` `k=3/20`
and `-1/4=6k` `=>` `k=-1/24`
The two values of `k` are different, so the `vecu` and `vecv` are not parallel.