Answer:
d=10u
Q(5/3,5/3,-19/3)
Step-by-step explanation:
The shortest distance between the plane and Po is also the distance between Po and Q. To find that distance and the point Q you need the perpendicular line x to the plane that intersects Po, this line will have the direction of the normal of the plane
, then r will have the next parametric equations:
![x=-5-2\lambda\\y=-5-2\lambda\\z=-3+\lambda](https://tex.z-dn.net/?f=x%3D-5-2%5Clambda%5C%5Cy%3D-5-2%5Clambda%5C%5Cz%3D-3%2B%5Clambda)
To find Q, the intersection between r and the plane T, substitute the parametric equations of r in T
![-2x-2y+z =-13\\-2(-5-2\lambda)-2(-5-2\lambda)+(-3+\lambda) =-13\\10+4\lambda+10+4\lambda-3+\lambda=-13\\9\lambda+17=-13\\9\lambda=-13-17\\\lambda=-30/9=-10/3](https://tex.z-dn.net/?f=-2x-2y%2Bz%20%3D-13%5C%5C-2%28-5-2%5Clambda%29-2%28-5-2%5Clambda%29%2B%28-3%2B%5Clambda%29%20%3D-13%5C%5C10%2B4%5Clambda%2B10%2B4%5Clambda-3%2B%5Clambda%3D-13%5C%5C9%5Clambda%2B17%3D-13%5C%5C9%5Clambda%3D-13-17%5C%5C%5Clambda%3D-30%2F9%3D-10%2F3)
Substitute the value of
in the parametric equations:
![x=-5-2(-10/3)=-5+20/3=5/3\\y=-5-2(-10/3)=5/3\\z=-3+(-10/3)=-19/3\\](https://tex.z-dn.net/?f=x%3D-5-2%28-10%2F3%29%3D-5%2B20%2F3%3D5%2F3%5C%5Cy%3D-5-2%28-10%2F3%29%3D5%2F3%5C%5Cz%3D-3%2B%28-10%2F3%29%3D-19%2F3%5C%5C)
Those values are the coordinates of Q
Q(5/3,5/3,-19/3)
The distance from Po to the plane
![d=\left| {\to} \atop {PoQ}} \right|=\sqrt{(\frac{5}{3}-(-5))^2+(\frac{5}{3}-(-5))^2+(\frac{-19}{3}-(-3))^2} \\d=\sqrt{(\frac{5}{3}+5))^2+(\frac{5}{3}+5)^2+(\frac{-19}{3}+3)^2} \\d=\sqrt{(\frac{20}{3})^2+(\frac{20}{3})^2+(\frac{-10}{3})^2}\\d=\sqrt{\frac{400}{9}+\frac{400}{9}+\frac{100}{9}}\\d=\sqrt{\frac{900}{9}}=\sqrt{100}\\d=10u](https://tex.z-dn.net/?f=d%3D%5Cleft%7C%20%7B%5Cto%7D%20%5Catop%20%7BPoQ%7D%7D%20%5Cright%7C%3D%5Csqrt%7B%28%5Cfrac%7B5%7D%7B3%7D-%28-5%29%29%5E2%2B%28%5Cfrac%7B5%7D%7B3%7D-%28-5%29%29%5E2%2B%28%5Cfrac%7B-19%7D%7B3%7D-%28-3%29%29%5E2%7D%20%5C%5Cd%3D%5Csqrt%7B%28%5Cfrac%7B5%7D%7B3%7D%2B5%29%29%5E2%2B%28%5Cfrac%7B5%7D%7B3%7D%2B5%29%5E2%2B%28%5Cfrac%7B-19%7D%7B3%7D%2B3%29%5E2%7D%20%5C%5Cd%3D%5Csqrt%7B%28%5Cfrac%7B20%7D%7B3%7D%29%5E2%2B%28%5Cfrac%7B20%7D%7B3%7D%29%5E2%2B%28%5Cfrac%7B-10%7D%7B3%7D%29%5E2%7D%5C%5Cd%3D%5Csqrt%7B%5Cfrac%7B400%7D%7B9%7D%2B%5Cfrac%7B400%7D%7B9%7D%2B%5Cfrac%7B100%7D%7B9%7D%7D%5C%5Cd%3D%5Csqrt%7B%5Cfrac%7B900%7D%7B9%7D%7D%3D%5Csqrt%7B100%7D%5C%5Cd%3D10u)
Answer:
x=-12
Step-by-step explanation:
32+2x=6+x+14
2x-x=6+14-32
x=-12
ST=6
TU=-12+14=2
SU=6+2=8
Answer:
3p-p
Step-by-step explanation:
I always think of the negative sign out ruling the positive sign so let's do that for the -p part.
3p-p is what it becomes
Your question says simplify but just in case you want the answer here it is:
-p is also the same as -1p
So therefore we have
3p-1p
And we subtract the coefficients and keep the variable
2p would be your answer but once again I don't know if you wanted that so just to be sure I put 3p-p as my "answer".