Question

Find the vector product axb. If a = 2i + 3j + 4k and b = 5i - 2j + k

11i + 18j - 19k
2j + 3k
5i - 6j + 7k
4i - 6j +11k

Answer 1

Answer on Question #46878 – Math – Vector Calculus

Find the vector product axb. If $a = 2i + 3j + 4k$ and $b = 5i - 2j + k$

Solution

$$\begin{array}{l} 11i + 18j - 19k \\ 2j + 3k \\ 5i - 6j + 7k \\ 4i - 6j + 11k \\ \end{array}$$

By the definition of vector product

$$\begin{array}{l} [a, b] = \begin{vmatrix} \boldsymbol{i} & \boldsymbol{j} & \boldsymbol{k} \\ 2 & 3 & 4 \\ 5 & -2 & 1 \end{vmatrix} = 3 \cdot 1 \cdot \boldsymbol{i} + 4 \cdot 5 \cdot \boldsymbol{j} + 2 \cdot (-2) \cdot \boldsymbol{k} - 3 \cdot 5 \cdot \boldsymbol{k} - 4 \cdot (-2) \cdot \boldsymbol{i} - 1 \cdot 2 \cdot \boldsymbol{j} = \\ = 11i + 18j - 19k \\ \end{array}$$

Answer: a

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