Find the equation of the vertical plane perpendicular to the y-axis and through the point (2, 3, 4).

Ok, the vector equation of a plane is:n∗(r−r0)=0where n is a vector normal to the plane, r is the position vector of an arbitrary point in the plane and r0 is the position vector of a given point in the plane. We need a normal vector to solve this. To get a normal vector, we use the given information that our plane is perpendicular to the y-axis. Therefore, our normal vector must be parallel to the y-axis. Any vector parallel to the y-axis will do, so I choose the unit vector <0,1,0> for simplicity. We have:<0,1,0>∗<x−2,y−3,z−4>=0giving,y=3This makes sense, since the y-coordinate must be constant, and there is no restriction on the values x,z that lie on the plane in 3-space.

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the law of definite proportions states samples of a compound will always contain the same proportion of elements by mass. in other words, a given compound will always contain the same elements in the same proportions by mass.the law of multiple proportions states when two elements combine with each other to form more than one compound, then the weights of one element that combine with a fixed weight of the other are in a ratio of small whole numbers.