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True or false p lies in plane b the line containing p and q must lie in plane b?
False. In order for the line PQ to lie in plane B, then both P and Q must lie in plane B.
Why does b times ab equal ab squared and not equal ab plus b squared?
b*ab = ab2 Suppose b*ab = ab + b2. Assume a and b are non-zero integers. Then ab2 = ab + b2 b = 1 + b/a would have to be true for all b. Counter-example: b = 2; a = 3 b(ab) = 2(3)(2) = 12 = ab2 = (4)(3) ab + b2 = (2)(3) + (2) = 10 but 10 does not = 12. Contradiction. So it cannot be the case that b = 1 + b/a is true for all b and, therefore, b*ab does not = ab + b2
Given two points A and B in the three dimensional space what is the set of points equidistant from A and B?
A plane is the set of all points in 3-D space equidistant from two points, A and B. If it will help to see it, the set of all points in a plane that are equidistant from points A and B in the plane will be a line. Extend that thinking off the plane and you'll have another plane perpendicular to the original plane, the one with A and B in it. And the question specified that A and B were in 3-D space. Another way to look at is to look at a line segment between A and B. Find the midpoint of that line segment, and then draw a plane perpendicular to the line segment, specifying that that plane also includes the midpoint of the line segment AB. Same thing. The set of all points that make up that plane will be equidistant from A and B. At the risk of running it into the ground, given a line segment AB, if the line segment is bisected by a plane perpendicular to the line segment, it (the plane) will contain the set of all points equidistant from A and B.
How to find area of rectangle on coordinate graph?
Suppose the sides of the rectangle ABCD are not parallel to the axis. Then if A = (p,q) and B = (r, s) then by Pythagoras, |AB|2 = (p - r)2 + (q - s)2 from which AB can be calculated. Calculate BC in a similar fashion and then area = AB*BC If AB is parallel to an axis (say the x axis), then q = s so that q - s = 0 and |AB|2 simplifies to (p - r)2 + 02 so that |AB| = |p - r|
Does A plus B equals AB?
No, A+B is left as A+B AB would be A x B
