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(a)[ Find a vector equation and parametric equations for the line that passes through the point A(5, 1, 4) and parallel to the line: x = -5t + 3, y = -t + 2, z = -2t + 2. (b)l Let A(-2, 5, x) and B(4, 7, -2) be two points in the three-dimensional space. Find the value of x such that the vectors OA and OB are orthogonal. (c)[Let x be the value found in part (b), and let C be the fourth vertex of the rectangle OACB. Find the area of this rectangle.

(a)[ Find a vector equation and parametric equations for the line that passes through the point A(5, 1, 4) and parallel to the line: x = -5t + 3, y = -t + 2, z = -2t + 2. (b)l Let A(-2, 5, x) and B(4, 7, -2) be two points in the three-dimensional space. Find the value of x such that the vectors OA and OB are orthogonal. (c)[Let x be the value found in part (b), and let C be the fourth vertex of the rectangle OACB. Find the area of this rectangle.

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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Work Problem 2 [3 (a)[.. Find a vector equation and parametric equations for the line that passes through the point A(5, 1, 4) and parallel to the line: x = -5t + 3, y = -t + 2, z = -2t + 2. (b)l Let A(-2, 5, x) and B(4, 7, -2) be two points in the three-dimensional space. Find the value of x such that the vectors OA and OB are orthogonal. (c)[Let x be the value found in part (b), and let C be the fourth vertex of the rectangle OACB. Find the area of this rectangle.
Transcribed Image Text:Work Problem 2 [3 (a)[.. Find a vector equation and parametric equations for the line that passes through the point A(5, 1, 4) and parallel to the line: x = -5t + 3, y = -t + 2, z = -2t + 2. (b)l Let A(-2, 5, x) and B(4, 7, -2) be two points in the three-dimensional space. Find the value of x such that the vectors OA and OB are orthogonal. (c)[Let x be the value found in part (b), and let C be the fourth vertex of the rectangle OACB. Find the area of this rectangle.
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