# 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

v1 =  2.1186
v2 =  -2.1186
v3 =  -1.2712
w1 =  -4.1186
w2 =  -1.8814
w3 =  -3.7288

### Step-by-step explanation:

${v}_{2}=\left(-2.1186\right)=-\frac{125}{59}=-2\frac{7}{59}=-2.1186$
${v}_{3}=\left(-1.2712\right)=-\frac{75}{59}=-1\frac{16}{59}=-1.2712$
${w}_{1}=\left(-4.1186\right)=-\frac{243}{59}=-4\frac{7}{59}=-4.1186$
${w}_{2}=\left(-1.8814\right)=-\frac{111}{59}=-1\frac{52}{59}=-1.8814$
${w}_{3}=\left(-3.7288\right)=-\frac{220}{59}=-3\frac{43}{59}=-3.7288$

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