Study guide and
3 practice problems
on:
Cross product and area of parallelograms
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The area of the parallelogram spanned by the vectors $\mathbf{x}$ and $\mathbf{y}$ is $| \mathbf{x} \times \mathbf{y}|$.
Related topics
Cross product
(17 problems)
Multivariable calculus
(147 problems)
Practice problems
Find the area of the triangle in 3-space between $(1,0,0)$, $(0,1,0)$, and $(0,0,1)$.
Solution
Consider the triangle in three-space given by $\langle a, 0, 0\rangle, \langle 0, b, 0 \rangle, \langle 0, 0, c \rangle.$ Find a vector that is perpendicular to the triangle and has length equal to the area of the triangle.
Solution
Sketch the parallelogram spanned by $\langle 1,1\rangle$ and $\langle 0, 1\rangle$. Use a cross product to find its area.
Solution