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

Nov 11, 2016

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, $\vec{u}$ and $\vec{v}$ are not ortogonal.

For $2$ vectors to be parallel, $\vec{u} = k \vec{v}$ where k is a scalar.
〈3/4,-1/4〉=k〈5,6〉
So, $\frac{3}{4} = 5 k$$\implies$$k = \frac{3}{20}$
and $- \frac{1}{4} = 6 k$$\implies$$k = - \frac{1}{24}$
The two values of $k$ are different, so the $\vec{u}$ and $\vec{v}$ are not parallel.