Euclidean space - computing distance
Not what you're looking for?
Compute the distance from a point b = (1, 0, 0, 1)^T to a line which passes through two points (0, 1, 1, 0)^T and (0, 1, 0, 2)^T. Here ^T denotes the operation of transposition, i.e. the points are represented by column-vectors instead of row-vectors.
Purchase this Solution
Solution Summary
This shows how to compute the distance from a point to a line with points represented by column vectors instead of row vectors.
Solution Preview
Let us sketch the picture. Obviously we cannot effectively draw vectors in 4-dimensional space, but the dimension in this problem is of little importance. We will sketch all the vectors in two dimensions to understand what's going on (see Attachment 1).
Let us introduce some notations: we will denote as v_0 the point (0, 1, 1, 0)^T and
as v the directional vector of the line L that passes through the two given
points, i.e.
v = (0, 1, 0, 2)^T - (0, 1, 1, 0)^T = (0, 0, -1, 2)^T;
Since the line does not pass though the origin, and hence, is not a subspace
we cannot use the straightforward ...
Purchase this Solution
Free BrainMass Quizzes
Solving quadratic inequalities
This quiz test you on how well you are familiar with solving quadratic inequalities.
Multiplying Complex Numbers
This is a short quiz to check your understanding of multiplication of complex numbers in rectangular form.
Know Your Linear Equations
Each question is a choice-summary multiple choice question that will present you with a linear equation and then make 4 statements about that equation. You must determine which of the 4 statements are true (if any) in regards to the equation.
Geometry - Real Life Application Problems
Understanding of how geometry applies to in real-world contexts
Probability Quiz
Some questions on probability