Study guide and
7 practice problems
on:
Cross product gives a perpendicular vector
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The cross product of two three-dimensional vectors is a three-dimensional vector perpendicular to both.
Related topics
Cross product
(17 problems)
Multivariable calculus
(147 problems)
Practice problems
Find a vector perpendicular to $\langle1, 2, 3 \rangle$.
Solution
Using a cross product, find a vector in 2d that is 90 degrees counterclockwise from $\langle a, b\rangle$.
Solution
Show that $\bfa \times \bfb$ is perpendicular to $\bfa$ by computing a dot product.
Solution
Find a unit vector perpendicular to $\langle 1, 1, 1\rangle$ and $\langle 1, 0, 1 \rangle.$
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
Find all the vectors in 3d that have unit length and are perpendicular to $$\Bigl(\frac{1}{\sqrt{2}}, \frac{1}{\sqrt{2}}, 0 \Bigr) \ \text{ and } \ \Bigl(0, \frac{1}{\sqrt{2}}, \frac{1}{\sqrt{2}} \Bigr).$$
Solution
Find the plane containing the points $(a,0,0)$, $(0, b, 0)$, and $(0,0,c)$.
Solution