Question

Question #cc952

Answer 1

`V = 3`

Explanation:

From the reference regarding a Parallelepiped, we obtain the formula for the volume:

#V = | | (u_1,u_2,u_3), (v_1,v_2,v_3), (w_1,w_2,w_3) | |#

This is the absolute value of the determinant of the vector components.

I will write the determinant:

#D = | (1,1,1), (1,0,1), (5,4,8) |#

I compute the determinant by repeating the first two columns:

#D = | (1,1,1,1,1), (1,0,1,1,0), (5,4,8,5,4) |#

Add the product of the major diagonals:

`(1)(0)(8)+(1)(1)(5)+(1)(1)(4)`

Subtract the product of the minor diagonals:

`(1)(0)(8)+(1)(1)(5)+(1)(1)(4) - (1)(0)(5)-(1)(1)(4)-(1)(1)(8)`

`D = -3`

The volume is the absolute value of the determinant:

`V = 3`