What is the cross product of $[1, - 4, 0]$ $[1, -4, 0]$ and $[4, 3, 6]$ $[4,3,6]$ ?

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What is the cross product of $[1, - 4, 0]$ $[1, -4, 0]$ and $[4, 3, 6]$ $[4,3,6]$ ?

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Answer 1 · 2016-06-01T12:45:22

It is $(- 24, - 6, 19)$ $(-24, -6, 19)$ .

Explanation:

The cross product of two vectors with coordinates

$v_{1} = (x_{1}, y_{1}, z_{1})$ $v_1=(x_1, y_1, z_1)$
$v_{2} = (x_{2}, y_{2}, z_{2})$ $v_2=(x_2, y_2, z_2)$

is defined as

$v_{1} \times v_{2} = (y_{1} z_{2} - z_{1} y_{2}, z_{1} x_{2} - x_{1} z_{2}, x_{1} y_{2} - y_{1} x_{2})$ $v_1\timesv_2=(y_1z_2-z_1y_2, z_1x_2-x_1z_2, x_1y_2-y_1x_2)$

We can apply this to our case

$v_{1} = (1, - 4, 0)$ $v_1=(1, -4, 0)$
$v_{2} = (4, 3, 6)$ $v_2=(4,3,6)$

$v_{1} \times v_{2} = (- 4 \cdot 6 - 0 \cdot 3, 0 \cdot 4 - 1 \cdot 6, 1 \cdot 3 - (- 4) \cdot 4)$ $v_1\times v_2=(-4*6-0*3, 0*4-1*6, 1*3-(-4)*4)$
$= (- 24, - 6, 19)$ $=(-24, -6, 19)$ .

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What is the cross product of $[1, - 4, 0]$ $[1, -4, 0]$ and $[4, 3, 6]$ $[4,3,6]$ ?

1 Answer

Explanation:

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Science

Math

Humanities

... and beyond

What is the cross product of [1,−4,0][1, -4, 0] and [4,3,6][4,3,6] ?

1 Answer

Explanation:

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What is the cross product of $[1, - 4, 0]$ $[1, -4, 0]$ and $[4, 3, 6]$ $[4,3,6]$ ?