Find a vector of magnitude 4 unit and parallel to vector I + j?

1 Answer

Answer:

#=2sqrt(2)*veci+2sqrt(2)vecj#

Explanation:

First we want to turn our given vector, #1*veci+1*vecj#, into a unit vector--which we do by dividing the vector by its own magnitude:

#||1 * veci+1* vecj|| = sqrt(1^2+1^2)=sqrt(2)#,

so the unit vector we want is:

#(1/sqrt(2))(1*veci+1*vecj)#

#=(1/sqrt(2))*veci+(1/sqrt(2))*vecj#

You might choose to rationalize this:

#=(sqrt(2)/2)*veci+(sqrt(2)/2)*vecj#

Now to get the vector we're looking for in the problem we have to scale our unit vector by a factor of 4:

#4((sqrt(2)/2)*veci+(sqrt(2)/2)*vecj)#

#=2sqrt(2)*veci+2sqrt(2)vecj#