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
v2=(2.1186)=2.1186
v3=(1.2712)=1.2712
w1=(4.1186)=4.1186
w2=(1.8814)=1.8814
w3=(3.7288)=3.7288



Did you find an error or inaccuracy? Feel free to write us. Thank you!



avatar







Tips to related online calculators
Our vector sum calculator can add two vectors given by their magnitudes and by included angle.
Do you have a system of equations and looking for calculator system of linear equations?

You need to know the following knowledge to solve this word math problem:

Related math problems and questions: