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## Homework Statement

Given the following 2-dimensional plane in R^4 written in parametric form:

x_1 = 1 + (-1)s

x_2 = 0 + ( 1)s

x_3 = 1 + (-1)t

x_4 = 0 + ( 1)t

a) find a 2-dimensional plane that does not intersect it

b) find a 2-dimensional plane that intersects it to form a point

c) find a 2-dimensional plane that intersects it to form a line

## Homework Equations

dot product

## The Attempt at a Solution

a) Just change the position vector, so what results is a parallel line, shifted away from the original plane, and therefore cannot intersect:

x_1 = 0 + (-1)s + (0)t

x_2 = 0 + (1)s + (0)t

x_3 = 0 + (0)s + (-1)t

x_4 = 0 + (0)s + (1)t

b) The dot product between the original plane and my new plane must be equal to zero, and hence they are perpendicular, forming a point. I'm not quite sure how to calculate this... Is this even possible (i.e., trick question)? Help!

c) I need the same position vector (1,0,1,0), but what about the direction vectors? I guess they shouldn't be perpendicular here, so... I'm really not sure... What if I change just one number in one of the direction vectors?

x_1 = 1 + (-1)s + (0)t

x_2 = 0 + (0)s + (0)t

x_3 = 1 + (0)s + (-1)t

x_4 = 0 + (0)s + (1)t

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