Are the vectors #v=4i+j# and #w=i-4j# parallel, orthogonal, or neither?

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Answer 1 · 2017-07-04T13:08:17

The vectors are orthogonal

Let's perform the check to see if they are parrallel

#vecv=kvecw#

So,

#((4),(1))=k((1),(-4))#

Therefore,

#4=1k#, #=>#, #k=4#

and

#1=-4k#, #=>#, #k=-1/4#

As #k# has different values, they are not parallel.

To see if they are orthogonal, we perform the dot product

#vecv.vecw= <4,1>.<1,-4> =(4*1)+(1*-4)=4-4=0#

As the dot product is #=0#, the vectors are orthogonal