Answer:
ü=2i+2j+0k
Step-by-step explanation:
The given plane 2x + 2y + 2 = 3 can also be written as:
2x+2y=3-2
2x+2y=1
The general equation for a plane is Ax+By+Cz=D and by definition the normal vector of that plane is n=Ai+Bj+Ck
Where i,j,k are the unit vectors
In order to demostrate that the vector n is normal to the plane, let R1=(a1,b1,c1) and R2=(a2,b2,c2) be two vectors that are in the plane.
If R1 ∈ Ax+By+Cz=D then Aa1+Bb1+Cc1=D
If R2 ∈ Ax+By+Cz=D then Aa2+Bb2+Cc2=D
Therefore, the vector R1R2=R2-R1=(a2-a1)i+(b2-b1)j+(c2-c1)k
You can apply the dot product. <em>If the dot product of the two vectors is zero then the vectors are normal.</em>
![R1R2_{o}n= [(a2-a1)i+(b2-b1)j+(c2-c1)k]_{o}(Ai+Bj+Ck)\\R1R2_{o}n = A(a2-a1) + B(b2-b1) + C(c2-c1)\\R1R2_{o}n = Aa2 + Bb2 +Cc2 - (Aa1+Bb1+Cc1)\\R1R2_{o}n = D - D\\R1R2_{o}n = 0](https://tex.z-dn.net/?f=R1R2_%7Bo%7Dn%3D%20%5B%28a2-a1%29i%2B%28b2-b1%29j%2B%28c2-c1%29k%5D_%7Bo%7D%28Ai%2BBj%2BCk%29%5C%5CR1R2_%7Bo%7Dn%20%3D%20A%28a2-a1%29%20%2B%20B%28b2-b1%29%20%2B%20C%28c2-c1%29%5C%5CR1R2_%7Bo%7Dn%20%3D%20Aa2%20%2B%20Bb2%20%2BCc2%20-%20%28Aa1%2BBb1%2BCc1%29%5C%5CR1R2_%7Bo%7Dn%20%3D%20D%20-%20D%5C%5CR1R2_%7Bo%7Dn%20%3D%200)
So, the vector which components are A,B,C is normal to the plane becase it is normal to any vector contained in the plane.
In this case:
A=2, B=2, C=0
ü=2i+2j+0k
It seems like you already have it but you haven't done the work all the way through yet. anyway Here:
Minutes: Students:
45 120
60 240
75 480
90 960
105 1000+
Answer:
2,100 people
Step-by-step explanation:
~Divide to find the number of people in fifths
3,500 / 5 = 700
~Multiply to find 2/5 of the total people
700 * 2 = 1,400
~Subtract to find the number of people against building the school.
3,500 - 1,400 = 2,100
Best of Luck!