Space vectors 3D

The vectors u = (1; 3; -4), v = (0; 1; 1) are given. Find the size of these vectors, calculate the angle of the vectors, the distance between the vectors.

Correct result:

a =  5.099
b =  1.4142
A =  13.8979 °
h =  5.4772

Solution:

u=(1,3,4) v=(0,1,1)  a=u=ux2+uy2+uz2=12+32+(4)2=26=5.099
b=v=vx2+vy2+vz2=02+12+12=2=1.4142
c=ux vx+uy+vy+uy vya b=1 0+3+1+3 15.099 1.41420.9707  A=180πarccos(c)=180πarccos(0.9707)=13.8979=135352"
w=uv w=(1,2,5)  h=w=wx2+wy2+wz2=12+22+(5)2=30=5.4772



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Tips to related online calculators
Our vector sum calculator can add two vectors given by its magnitudes and by included angle.
Pythagorean theorem is the base for the right triangle calculator.
Cosine rule uses trigonometric SAS triangle calculator.
See also our trigonometric triangle calculator.

 
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