I think the best answer would be answer D
Answer:
![(\frac{1}{2},\frac{-1}{2},\frac{1}{2})](https://tex.z-dn.net/?f=%28%5Cfrac%7B1%7D%7B2%7D%2C%5Cfrac%7B-1%7D%7B2%7D%2C%5Cfrac%7B1%7D%7B2%7D%29)
Step-by-step explanation:
We have been given the intersection coordinates:
(7,1,-6) and perpendicular to the line x=-1+t ,y=-2+t and z=-1+t
From the condition of perpendicularity we know:
![(7,1,-6)(x,y,z)](https://tex.z-dn.net/?f=%287%2C1%2C-6%29%28x%2Cy%2Cz%29)
![\Rightarrow 7x+y-6z=0](https://tex.z-dn.net/?f=%5CRightarrow%207x%2By-6z%3D0)
Now, we have given x=-1+t , y=-2+t and z= -1+t
![7(-1+t)+(-2+t)-6(-1+t)=0](https://tex.z-dn.net/?f=7%28-1%2Bt%29%2B%28-2%2Bt%29-6%28-1%2Bt%29%3D0)
![-7+7t-2+t+6-6t=0](https://tex.z-dn.net/?f=-7%2B7t-2%2Bt%2B6-6t%3D0)
![\Rightarrow -3+2t=0](https://tex.z-dn.net/?f=%5CRightarrow%20-3%2B2t%3D0)
![2t=3](https://tex.z-dn.net/?f=2t%3D3)
![t=\frac{3}{2}](https://tex.z-dn.net/?f=t%3D%5Cfrac%7B3%7D%7B2%7D)
Now, substituting t in the given coordinates x,y and z we get:
![x=-1+\frac{3}{2}=\frac{1}{2}](https://tex.z-dn.net/?f=x%3D-1%2B%5Cfrac%7B3%7D%7B2%7D%3D%5Cfrac%7B1%7D%7B2%7D)
![y=-2+\frac{3}{2}=\frac{-1}{2}](https://tex.z-dn.net/?f=y%3D-2%2B%5Cfrac%7B3%7D%7B2%7D%3D%5Cfrac%7B-1%7D%7B2%7D)
And ![z=-1+\frac{3}{2}=\frac{1}{2}](https://tex.z-dn.net/?f=z%3D-1%2B%5Cfrac%7B3%7D%7B2%7D%3D%5Cfrac%7B1%7D%7B2%7D)
The volume of a rectangular prism is always LWH=V, the cube is a special prism in that L=W=H are all equal so:
V=s^3 where s is the length of all sides...
s^3=1728
s=1728^(1/3)
s=12 units
Answer: 72
Step-by-step explanation: Because if you do 18 + 24 + 30