Answer:
Angle between the given vectors is approximately 100.89 degrees.
Step-by-step explanation:
We are given the following in the question:
[tex]a=[0,1,1], B=[1,2,-3][/tex]
We have to find angle between the two vectors.
First we evaluate the dot product for the given vectors.
[tex]a.b = (0.1) + (1.2) + (1.-3) \\=-1[/tex]
The magnitude of the vectors can be calculated in the following manner
[tex]|a| = \sqrt{0^2 + 1^2 + 1^2} = \sqrt{2}\\|b| = \sqrt{1^2 + 2^2 + (-3)^2} = \sqrt{14}[/tex]
Formula:
[tex]a.b = |a| |b| \cos \theta\\\text{where theta is the angle between the two vectors}[/tex]
Putting the values, we get,
[tex]-1 = (\sqrt2)(\sqrt{14})\cos \theta\\\\\cos \theta = \displaystyle\frac{-1}{2\sqrt7}\\\\\theta = \arccos(\frac{-1}{2\sqrt7})\\\\\theta \approx 1.76\text{ radians}\\\theta \approx 100.89\text{ degrees}[/tex]
Angle between the given vectors is approximately 100.89 degrees.
