Rectangular prism is defined by vectors (2,0,0)(0,9,5) and (0,0,3). Find the volume.

I have done this so far, would anyone please verify this.

(2,0,0)(0,9,6)

(0-2, 9-0, 6-0)
=(-2,9,6)

(-2,9,6)(0,0,3)

=(2,-9,-3)

(2)(-9)(-3)=54 cm^3

Therefore volume is 54 cm^3

54 cm^3 is the correct answer

I do it differently:
if given 3 vectors a, b, and c
volume of parallelepiped
=| a . (b X c) |

(2,0,0) X (0,0,3) = (0, -6, 0)

volume = |(0,9,5) . (0,-6,0) |
= |0-54+0| = 54

Thank you very much!

To find the volume of a rectangular prism defined by vectors, you need to use the cross product of the two vectors.

First, take the cross product of the two vectors (2,0,0) and (0,9,5):

(2,0,0) x (0,9,5) = (0*(-5) - 0*(9), -2*(5) - 0*(0), 2*(9) - 0*(0))
= (0, -10, 18)

Now, take the dot product of the resulting vector (0, -10, 18) with the third given vector (0, 0, 3):

(0, -10, 18) . (0, 0, 3) = 0*(0) + (-10)*(0) + 18*(3)
= 0 + 0 + 54
= 54

Therefore, the volume of the rectangular prism is 54 cubic units (cm^3 in this case).

Your answer of 54 cm^3 is correct.