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

Question

1334 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-05-16T14:06:35

$a$ $a$ x $b = - 10 i - 8 j + 3 k$ $b=-10i-8j+3k$

Let vector $a = 2 \cdot i - 1 \cdot j + 4 \cdot k$ $a=2*i-1*j+4*k$ and $b = - 1 \cdot i + 2 \cdot j + 2 \cdot k$ $b=-1*i+2*j+2*k$

The formula for cross product

$a$ $a$ x $b=[(i,j,k),(a_1,a_2,a_3),(b_1,b_2,b_3)]$

$a$ x $b=+a_2b_3i+a_3b_1j+a_1b_2k-a_2b_1k-a_3b_2i-a_1b_3j$

Let us solve the cross product

$a$ x $b=[(i,j,k),(2, -1, 4),(-1, 2, 2)]$

$a$ x $b=$

$+(-1)(2)i+(4)(-1)j+(2)(2)k-(-1)(-1)k-(4)(2)i-(2)(2)j$

$a$ x $b=-2*i-8i-4j-4j+4k-1*k$

$a$ x $b=-10i-8j+3k$

God bless...I hope the explanation is useful.

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