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.