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

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

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Answer 1 · 2016-01-27T12:12:04

$[6, 14, - 11]$ $[6,14,-11]$

Explanation:

Since cross product is distributive, you can "expand" it

$(- ˆ i + 2 ˆ j + 2 ˆ k) \times (4 ˆ i + 3 ˆ j + 6 ˆ k)$ $(-hati + 2hatj + 2hatk) xx (4hati + 3hatj + 6hatk)$

$= (- ˆ i) \times (4 ˆ i) + (- ˆ i) \times (3 ˆ j) + (- ˆ i) \times (6 ˆ k)$ $= (-hati)xx(4hati) + (-hati)xx(3hatj) + (-hati)xx(6hatk)$
$+ (2 ˆ j) \times (4 ˆ i) + (2 ˆ j) \times (3 ˆ j) + (2 ˆ j) \times (6 ˆ k)$ $+ (2hatj)xx(4hati) + (2hatj)xx(3hatj) + (2hatj)xx(6hatk)$
$+ (2 ˆ k) \times (4 ˆ i) + (2 ˆ k) \times (3 ˆ j) + (2 ˆ k) \times (6 ˆ k)$ $+ (2hatk)xx(4hati) + (2hatk)xx(3hatj) + (2hatk)xx(6hatk)$

$= 0 - 3 ˆ k + 6 ˆ j$ $= 0 - 3hatk + 6hatj$
$- 8 ˆ k + 0 + 12 ˆ i$ $- 8hatk + 0 + 12hati$
$+ 8 ˆ j - 6 ˆ i + 0$ $+ 8hatj - 6hati + 0$

$= 6 ˆ i + 14 ˆ j - 11 ˆ k$ $= 6hati + 14hatj - 11hatk$

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

1 Answer

Explanation:

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

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