Question

Consider the vectors : u =( 2, 3, 5), and v = (1, 2,4)

Find an equation of a plane containing u and v

Answer 1

cross your vectors to define the normal to the plane, then use either vector as the point to anchor it to

Answer 2

spose uxv = (a,b,c)

the you can define the plane as: a(x-ux) + b(y-uy) + c(z-uz) = 0

or use the v parts instead of u parts same same

Answer 3

you have responded to my real question , I guess. Can we treat vectors as points? I could not do it confidently...but its the only way and only meaningful thing one can do i guess?

Answer 4

vectors are not confined to one place. the represent a direction and a distance.

spose u describes a vector between the points A and B arbitrarily on space. the position vector that is equivalent to u is the vector from (A-A) and (B-A), which is from <0> to some relative point that b is moved to.

As such, the vector u and v are thought of as being anchored to the origin and terminating at some given point which makes a point and a vector as far as notation goes, the same thing.

Answer 5

using A and B as just generic points and not as before .... we see that the plane that contains u and v, is the same that contains the points A,B and the origin O