Context: Find the volume of the following parallelepiped, given the vertices of the 3d model: Front bottom right corner - (-2,4,5), front bottom left corner - (-2,1,4), back bottom left corner - (-5,1,4), front top left corner - (-2,2,7). use grade 12 knowledge Answer question

To find the volume of a parallelepiped, we need to find the vectors of the three edges that meet at a point, and then calculate the scalar triple product of these vectors.

Let's denote the vertices as follows: A: Front bottom right corner (-2,4,5) B: Front bottom left corner (-2,1,4) C: Back bottom left corner (-5,1,4) D: Front top left corner (-2,2,7)

We can form three vectors from these points: AB: B - A = (-2-(-2), 1-4, 4-5) = (0, -3, -1) AC: C - A = (-5-(-2), 1-4, 4-5) = (-3, -3, -1) AD: D - A = (-2-(-2), 2-4, 7-5) = (0, -2, 2)

The volume V of the parallelepiped is given by the absolute value of the scalar triple product of these vectors, which is the determinant of the 3x3 matrix formed by the vectors:

V = |AB.AC.AD| = |0 -3 -1| |-3 -3 -1| |0 -2 2|

Calculating the determinant, we get:

V = 0*(-3*-1 - -22) - -3(-3*-1 - 02) + -1(-3*-2 - 00) V = 0(3 - -4) - -3*(3 - 0) + -1*(-6 - 0) V = 0*7 - -9 + 6 V = 0 + 9 + 6 V = 15 cubic units

So, the volume of the parallelepiped is 15 cubic units.