Study guide and
2 practice problems
on:
The angle between two vectors is always between zero and pi
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The angle between vectors is always between 0 and $\pi$, inclusive.
It is $0$ if the vectors are in the same direction.
It is $\pi$ if the vectors are in opposite directions.
Related topics
Angle between vectors
(7 problems)
Vectors
(55 problems)
Multivariable calculus
(147 problems)
Practice problems
Prove that $\bfx \cdot \bfx = \left| \bfx \right|^2$ in two ways:
Directly (in the case of 3d vectors)
By the dot product angle formula
Solution
What is the angle between a nonzero vector $\bfx$ and $-\bfx$? Use that angle to show that $\bfx \times (-\bfx)=0$.
Solution