What is the cross product of $[3, 2, 5]$ $[3, 2, 5]$ and $[- 1, 2, 2]$ $[-1, 2, 2]$ ?

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Answer 1 · 2016-05-14T07:40:53

$a x b = - 6 i - 11 j + 8 k$ $color(blue)(a " x " color(blue)(b=-6i-11j+8k)$

Let vector $a = 3 \cdot i + 2 \cdot j + 5 \cdot k$ $a=3*i+2*j+5*k$ 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 $b=[(i,j,k),(3, 2, 5),(-1, 2, 2)]$

$a$ x $b=$

$+(2)(2)i+(5)(-1)j+(3)(2)k-(2)(-1)k-(5)(2)i-(3)(2)j$

$a$ x $b=+4*i-10i-5j-6j+6k+2k$

$a$ x $b=-6i-11j+8k$

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

What is the cross product of [3, 2, 5][3,2,5][3, 2, 5] and [-1, 2, 2] [−1,2,2][-1, 2, 2] ?