Question

What is the cross product of `<4 , 5 ,0 >` and `<4, 1 ,-2 >`?

Answer 1

`< -10, -8, -16>`

Explanation:

We'll call the vector `< 4, 5, 0 > vec A`, and the vector `< 4, 1, -2> vec B`

The cross product of `vec A` and `vec B` is a vector `vec C` with components

`C_x = A_yB_z - A_zB_y`

`C_y = A_xB_z - A_zB_x`

`C_z = A_xB_y - A_yB_x`

We have our components for vectors `vec A` and `vec B` expressed in their position vectors, and we'll use these values to calculate the components of `vec C`:

`C_x = (5)(-2) - (0)(1) = -10`

`C_y = (4)(-2) - (0)(4) = -8`

`C_z = (4)(1) - (5)(4) = -16`

Using unit vectors, this vector product `vec C` is

`(-10)vec i + (-8)vec j + (-16)vec k`

Or, expressed as a position vector,

`< -10, -8, -16>`