Study guide and
3 practice problems
on:
Cross product length and the angle between vectors
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If $\bfx$ and $\bfy$ are vectors and $\theta$ is the angle between them, then the length of their cross product is $$| \bfa \times \bfb | = | \bfa | | \bfb| \sin(\theta)$$
Two vectors have zero cross product if they are multiples of each other.
Related topics
Cross product
(17 problems)
Multivariable calculus
(147 problems)
Practice problems
If $\bfi \times \bfx = \bfi \times \bfy$, does $\bfx = \bfy$? If so, prove it. If not, find a counterexample.
Solution
Compute $\bfi \times (\bfi + \bfk)$ in two ways:
By the determinant formula
By expanding the sum and recalling the cross products of standard coordinate vectors with each other
Solution
What is the angle between a nonzero vector $\bfx$ and $-\bfx$? Use that angle to show that $\bfx \times (-\bfx)=0$.
Solution