Multivariable Calculus - Scalar projection

[Larrytsai]

Homework Statement

Find the scalar and vector projection of the vector b=(3,5,3) onto the vector a=(0,1,-5) .

Homework Equations

The Attempt at a Solution

What I've tried is multiplying all the i's and j's and k's together and adding up everything because you get a scalar answer in the end so basically...

3*0 + 1*5 + 3*(-5)
= -10
then i tried to divide by the magnitude of vector |a|

|a|=sqrt(26)

so i get scalar projection as -10/(sqrt(26)) as my answer

 

[Dick]

Ok, so the scalar projection is b.a/|a|. That seems ok. What's your question?

 

[Larrytsai]

Can you please explain why we divide by the magnitude of vector "a" and if my work is correct or not please?

 

[Dick]

Can you please explain why we divide by the magnitude of vector "a" and if my work is correct or not please?

The scalar projection should be |b|*cos(theta) where theta is the angle between a and b. Since the dot product is given by (a.b)=|a||b|cos(theta) the scalar projection should be (a.b)/|a|. Yes, you are doing fine so far.