What is the projection of $(3i + 2j - 3k)$ onto $( i - j + k)$ ?

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Answer 1 · 2017-01-31T06:12:59

$< -2/3, 2/3, -2/3 >$

The projection of vector a onto b is...
$( a*b )/| b |^2*b$

In this case, a is < 3, 2,-3 > and b is < 1, -1, 1 >. Plug in these vectors and simplify...

$(< 3, 2,-3 > * < 1, -1, 1 >)/|< 1, -1, 1 >|^2*b$

$(3*1+2*(-1)+(-3)*1)/((sqrt(1^2+(-1)^2+1^2))^2)*b$

$(3-2-3)/sqrt(3)^2*< 1, -1, 1 >$

$-2/3*< 1, -1, 1 >$

$< -2/3, 2/3, -2/3 >$

What is the projection of (3i + 2j - 3k)(3i + 2j - 3k) onto ( i - j + k) ( i - j + k)?