Question

Let a = 2i - j and b = i + j + k , evaluate a x b.
3k+2j-i
i +2j+3k
3k-2j-i
i+2j-3k

Answer 1

Answer on Question #52180 – Math – Vector Calculus

Question

Let $a = 2i - j$ and $b = i + j + k$, evaluate $a \times b$.

$$3k + 2j - i \\ i + 2j + 3k$$ $$3k - 2j - i \\ i + 2j - 3k$$

Solution

If $a = 2i - j$ and $b = i + j + k$, then the cross product $a \times b$ is

$$\begin{array}{l} a \times b = \left| \begin{array}{ccc} i & j & k \\ 2 & -1 & 0 \\ 1 & 1 & 1 \end{array} \right| = i \left| \begin{array}{cc} -1 & 0 \\ 1 & 1 \end{array} \right| - j \left| \begin{array}{cc} 2 & 0 \\ 1 & 1 \end{array} \right| + k \left| \begin{array}{cc} 2 & -1 \\ 1 & 1 \end{array} \right| \\ = i(-1 * 1 - 1 * 0) - j(2 * 1 - 1 * 0) + k(2 * 1 - 1)(-1)) = -i - 2j + 3k. \end{array}$$

Answer: $a \times b = 3k - 2j - i$.

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