3. Pick three non-collinear points A, B, and C (e.g., A(2, -1,2), B(-3, 4, 0), C(1, 3, 2)). Determine thefollowing quantities. (a) Lengths of all sides of the triangle ABC.(b) Both types (vector and parametric) of equations of the line passing through A and B.(c) Both types (vector and parametric) of equations of the line segment from B (t = 0) to C (t = 1).(d) An equation of a line through C parallel to the line through A and B.1

Answered: Lengths of all sides of the triangl…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

3. Pick three non-collinear points A, B, and C (e.g., A(2, -1,2), B(-3, 4, 0), C(1, 3, 2)). Determine the
following quantities.

(a) Lengths of all sides of the triangle ABC.
(b) Both types (vector and parametric) of equations of the line passing through A and B.
(c) Both types (vector and parametric) of equations of the line segment from B (t = 0) to C (t = 1).
(d) An equation of a line through C parallel to the line through A and B.
1

Expert Solution

Step 1

Here, in the question, we have to pick three non-collinear points $A, B & C$ $(A (2, - 1, 2), B (- 3, 4, 0), C (1, 3, 2)$ . We have to determine the quantities given in parts. The non-collinear points do not lie on the same straight line then they are said to be non-collinear points. If any points of the given points are not on the same line then as a group of same collinear points.

The vector equation's components, $x = x_{0} + a t$ , $y = y_{0} + b t$ , and $z = z_{0} + c t$ , are the line's parametric equations. The direction numbers of the line are the three elements $a, b,$ and $c$ .