What is the cross product of $[1, - 2, - 1]$ $[1,-2,-1]$ and $[4, 3, 6]$ $[4,3,6]$ ?

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Answer 1 · 2016-05-22T00:19:48

The cross product is ${- 9, - 10, 11}$ ${-9,-10,11}$ .

For two vectors ${a, b, c}$ ${a,b,c}$ and ${x, y, z}$ ${x,y,z}$ , the cross product is given by:

${(b z - c y), (c x - a z), (a y - b x)}$ ${(bz-cy),(cx-az),(ay-bx)}$

In this case, the cross product is:

${(- 2 \cdot 6) - (- 1 \cdot 3), (- 1 \cdot 4) - (1 \cdot 6), (1 \cdot 3) - (- 2 \cdot 4)}$ ${(-2*6)-(-1*3),(-1*4)-(1*6),(1*3)-(-2*4)}$

$= {(- 12) - (- 3), (- 4) - (6), (3) - (- 8)}$ $={(-12)-(-3),(-4)-(6),(3)-(-8)}$

$= {- 9, - 10, 11}$ $={-9,-10,11}$

What is the cross product of [1,-2,-1][1,−2,−1][1,-2,-1] and [4,3,6] [4,3,6][4,3,6] ?