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I would like to know if my problem is correct. It is a homework from my university course.

The questions are:

a) Find the projection of $y$ on $x$
b) Find the vector projection of $y$ on $x$
c) Find the vector projection of $y$ on the normal of $x$
where $x = [5,2,-1]$, $y = [0,1,1]$

a)

$P = \frac{[0,1,1] \cdot [5,2,-1]}{\sqrt{30}} = √30 / 30 *(-5) = -3√30 / 18$

b)

$yx = -3√30 / 18 * √30 / 30 [5,2,-1] = -3 / 18 [5,2,-1] = [-15/18,-6/18,3/18]$

c)

$y \perp x = [0,1,1] - [-15/18,-6/18,3/18] = [15/18,4/3,15/18]$

  • 1
    For starters, $x\cdot y = 5*0 + 2*1 + (-1)*1 \neq -5$.2012-11-01
  • 0
    What is the difference between questions a) and b)?2012-11-01
  • 0
    Just to way to rewrite it2012-11-01

1 Answers 1