A rectangular prism is defined by vectors (2,0,0) (0,9,6) and (0,0,3). Find the volume.

Expert Answers
sciencesolve eNotes educator| Certified Educator

You need to remember that you may find the volume of rectangular prism evaluating the product of the area of base( length multiplied by width) and height of the prism.

You need to evaluate the measure of length of prism such that:

`L = sqrt((0-2)^2 + (9-0)^2 + (6-0)^2) `

`L = sqrt(4 + 81+ 36)`

`L = sqrt121 `

`L = 11`

You need to evaluate the measure of width of prism such that:

`w = sqrt((0-0)^2 + (9-0)^2 + (6-3)^2) `

`w = sqrt(81 + 9) `

`w = sqrt90`

`w = 3sqrt10`

You need to evaluate the measure of height of prism such that:

`h = sqrt((0-2)^2 + (0-0)^2 + (3-0)^2)`

`h = sqrt(4+9)`

`h = sqrt13`

You may evaluate the volume of rectangular prism such that:

`V = L*w*h`

`V = 11*3sqrt10*sqrt13`

`V = 33sqrt130`

Hence, evaluating the volume of rectangular prism yields `V = 33sqrt130.`