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

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

#### Explanation:

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

The formula for cross product

$a$x$b = \left[\begin{matrix}i & j & k \\ {a}_{1} & {a}_{2} & {a}_{3} \\ {b}_{1} & {b}_{2} & {b}_{3}\end{matrix}\right]$

$a$x$b = + {a}_{2} {b}_{3} i + {a}_{3} {b}_{1} j + {a}_{1} {b}_{2} k - {a}_{2} {b}_{1} k - {a}_{3} {b}_{2} i - {a}_{1} {b}_{3} j$

Let us solve the cross product

$a$x$b = \left[\begin{matrix}i & j & k \\ 2 & - 1 & 4 \\ - 1 & 2 & 2\end{matrix}\right]$

$a$x$b =$

$+ \left(- 1\right) \left(2\right) i + \left(4\right) \left(- 1\right) j + \left(2\right) \left(2\right) k - \left(- 1\right) \left(- 1\right) k - \left(4\right) \left(2\right) i - \left(2\right) \left(2\right) j$

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

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

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