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(e) An equation of the plane passing through A, B, and C. (f) An equation of the line passing through C and normal to the plane through A, B, C. (g) The area of the triangle ABC; the area of the parallelogram whose two sides are AB and AC.

(e) An equation of the plane passing through A, B, and C. (f) An equation of the line passing through C and normal to the plane through A, B, C. (g) The area of the triangle ABC; the area of the parallelogram whose two sides are AB and AC.

Advanced Engineering Mathematics
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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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.
Transcribed Image Text: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.
(e) An equation of the plane passing through \(A\), \(B\), and \(C\). (f) An equation of the line passing through \(C\) and normal to the plane through \(A\), \(B\), \(C\). (g) The area of the triangle \(ABC\); the area of the parallelogram whose two sides are \(AB\) and \(AC\). (h) The distance between the point \(C\) and the line passing through \(A\) and \(B\). (i) Parametric equations of the circle with center \(A\), passing through \(C\), and lying in the plane \(z = 2\). (Make the orientation such that the projection of the circle into the \(xy\)-plane has positive orientation counterclockwise.)
Transcribed Image Text:(e) An equation of the plane passing through \(A\), \(B\), and \(C\). (f) An equation of the line passing through \(C\) and normal to the plane through \(A\), \(B\), \(C\). (g) The area of the triangle \(ABC\); the area of the parallelogram whose two sides are \(AB\) and \(AC\). (h) The distance between the point \(C\) and the line passing through \(A\) and \(B\). (i) Parametric equations of the circle with center \(A\), passing through \(C\), and lying in the plane \(z = 2\). (Make the orientation such that the projection of the circle into the \(xy\)-plane has positive orientation counterclockwise.)
Expert Solution
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Since you have posted a question with multiple sub-parts, so we will solve only the first three sub-parts for you. Kindly repost the others in the next question.

Let us consider the three non-collinear points A,B and C be:

                  A2,-1,2, B-3,4,0, C1,3,2

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