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 answer:

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

Step-by-step explanation:

u=(1,3,4) v=(0,1,1)  a=u=ux2+uy2+uz2=12+32+(4)2=26=5.099
c=a bux vx+uy+vy+uy vy=5.099 1.41421 0+3+1+3 10.9707  A=π180°arccos(c)=π180°arccos(0.9707)=13.8979=13°5352"
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 their 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.

We encourage you to watch this tutorial video on this math problem: video1   video2

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