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

1 Answer
Narad T.
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, #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.

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