Question #324973

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

1
Expert's answer
2022-04-07T12:26:33-0400

It is not stated anything regarding the magnitude of a vector. We assume that the vector is a cross product of vectors AA and BB. The cross product is perpendicular to both vectors. Namely, we have C=ijka1a2a3b1b2b3=a2a3b2b3ia1a3b1b3j+a1a2b1b2kC=\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=(a2a3b2b3)2+(a1a3b1b3)2+(a1a2b1b2)2|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}



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