Answer to Question #324973 in Analytic Geometry for Agenda

Question

Find the vector C of magnitude c that is perpendicular to vectors A=a1i + a2j + a3k and B=b1i + b2j + b3k

Answer 1

It is not stated anything regarding the magnitude of a vector. We assume that the vector is a cross product of vectors $A$ and $B$. The cross product is perpendicular to both vectors. Namely, we have $C=\left|\begin{array}{lll}i&j&k\\a_1&a_2&a_3\\b_1&b_2&b_3\end{array}\right|=\left|\begin{array}{ll}a_2&a_3\\b_2&b_3\end{array}\right|i-\left|\begin{array}{ll}a_1&a_3\\b_1&b_3\end{array}\right|j+\left|\begin{array}{ll}a_1&a_2\\b_1&b_2\end{array}\right|k$

The magnitude is $|C|=\sqrt{\left(\left|\begin{array}{ll}a_2&a_3\\b_2&b_3\end{array}\right|\right)^2+\left(\left|\begin{array}{ll}a_1&a_3\\b_1&b_3\end{array}\right|\right)^2+\left(\left|\begin{array}{ll}a_1&a_2\\b_1&b_2\end{array}\right|\right)^2}$