# (b) Let vector y be the vector of length 8 and in the opposite direction as vector v= <1,1,0> What is vector y equal to?

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### 1 Answer

First, the vector <1,1,0> has length

`sqrt(1^2+1^2+0^2)=sqrt(2)`

If we wanted it to have length 8, we would need to multiply each entry by `8/sqrt(2)`

Thus, a vector in the same direction as v, but with length 8, would be:

`<8/sqrt(2),8/sqrt(2),0>`

This simplifies to:

`<4 sqrt(2), 4 sqrt(2), 0>`

To get a vector that is the same length but in the opposite direction, multiply each entry by -1:

`<-4 sqrt(2), -4 sqrt(2), 0>`

This vector has length 8, but is in the opposite direction of v