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

1 Answer
May 24, 2017

Answer:

#< -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>#