# Suppose vector u = <5,1,-4> and vector v = <-1,0,1>a) Find the projection of vector u along vector v

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Expert Answers

sciencesolve | Certified Educator

You need to remember the equation that gives the projection of vector `bar u` along vector `bar v` , such that:

`bar u_v = (bar u*bar v)/(|barv|^2)*bar v`

You need to remember how to perform the multiplication of two vectors, such that:

`bar u = a*bari + b*bar j + c*bar k`

`bar v = m*bari + n*bar j + p*bar k`

`bar u*bar v = a*m + b*n + c*p`

Reasoning by analogy yields:

`bar u*bar v = 5*(-1) + 1*0 + (-4)*1 => bar u*bar v = -9`

`|bar v| = sqrt((-1)^2 + 0^2 + 1^2)`

`|bar v| = sqrt2 => (|barv|^2) = 2`

`bar u_v = (-9/2)*<-1,0,1> => bar u_v = <9/2,0,-9/2>`

**Hence, evaluating the projection of vector `bar u` along vector `bar v` yields **`bar u_v = <9/2,0,-9/2>.`