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 answer:

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

Step-by-step explanation:

a=(5,5,3) b=(2,4,5)  b=v+w va=>v=ka  wa=>w.a=0  2=v1+w1 4=v2+w2 5=v3+w3 v1=5 k v2=5 k v3=3 k w1 (5)+w2 5+w3 3=0  v1+w1=2 v2+w2=4 v3+w3=5 5k+v1=0 5kv2=0 3kv3=0 5w15w23w3=0  k=59250.423729 v1=591252.118644 v2=591252.118644 v3=59751.271186 w1=592434.118644 w2=591111.881356 w3=592203.728814

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