# Parallel and orthogonal

I need math help in this problem: a=(-5, 5 3) b=(-2,-4,-5) (they are vectors)
Decompose the vector b into b=v+w where v is parallel to a and w is orthogonal to a, find v and w

Correct result:

v1 =  0
v2 =  0
v3 =  0
w1 =  0
w2 =  0
w3 =  0

#### Solution:

$a=(-5, 5, 3) \ \\ b=(-2,-4,-5) \ \\ \ \\ b=v+w \ \\ v \parallel a=> v=k a \ \\ \ \\ w \perp a=> w.a=0 \ \\ \ \\ \ \\ v_{1}=<\div class='alert alert-danger'>System of equations are non-linear. <\div class='alert alert-danger'>Sorry, equation/equations do not have an integer solution ... Please check them.=0$
$v_{2}=0$
$v_{3}=0$
$w_{1}=0$
$w_{2}=0$
$w_{3}=0$

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