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October 24, 2016
Posted by **mo** on Saturday, April 4, 2009 at 9:42am.

can anyone explian it to me plezzz

- calculus -
**mo**, Saturday, April 4, 2009 at 9:52amDetermine whether the plane passing through the points A(1,2,3) , B(0,1,0) and C(0,2,2) passes through the origin

- calculus -
**mo**, Saturday, April 4, 2009 at 9:53amWhat does the following equation represent in R^3 ? Justify your answer.

x=y=z

- calculus -
- calculus -
**Count Iblis**, Saturday, April 4, 2009 at 9:55amThat's the distance from the point

p1 = (0, 0, z) to p2 = (x, y, z).

The square of the distance is the square of the norm of the difference of p1 and p2, which is the inner product of that difference vector with itself (also conventionally denoted as the square of the vector):

d^2 = (p1-p2)^2 = x^2 + y^2 - calculus -
**Count Iblis**, Saturday, April 4, 2009 at 10:42amQuastion:

Determine whether the plane passing through the points A(1,2,3) , B(0,1,0) and C(0,2,2) passes through the origin.

Let's perform a translation, so that B moves to the origin and the old origin moves to minus B:

A = (1,1,3)

C = (0,1,2)

(I prefer this notation instead of writing A(x,y,z), so I consider A, B, C etc as vectors).

The location of the old origin is denoted by X:

X = (0,-1,0)

If X can be written as a linear combination of A and C, then X is on the plane. So, what you need to do is to determine the rank of the matrix which has A, B and X as its rows (or columns).

I find that the rank is 3, so X is not a point on the plane. - calculus -
**Reiny**, Saturday, April 4, 2009 at 11:11am>> Determine whether the plane passing through the points A(1,2,3) , B(0,1,0) and C(0,2,2) passes through the origin. <<

alternate method:

vector AB = (1,1,2)

vector AC = (1,0,1)

normal to these is (1,1,-1) , I took the cross-product

so the equation of the plane is

x + y - z = k

put in (1,2,3) , or any of the other two points,

1 + 2 - 3 = k = 0

plane equation is x + y - z = 0

and the point (0,0,0) satisfies this - calculus -
**Reiny**, Saturday, April 4, 2009 at 11:24am>> What does the following equation represent in R^3 ? Justify your answer.

x=y=z <<

suppose I rewrote the statement this way

(x-0)/1 = (y-0)/1 = (z-0)/1

does that help?