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Please do a, b, c,

Please do a, b, c,

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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Please do a, b, c, d and e

14. Lines on a Plane in Space. Suppose that L is a line in Cartesian space, and II is a plane in Cartesian space. We will say that L is on II, or L c II if every point on L is also a point on II. This means that the coordinates of every point on L must satisfy the Cartesian equation of II. Show that the line with vector equation (x, y, z) = t(3, 5,–3) is on the plane 7x — Зу + 2z 3D 0. Show that the line Span({9,-3, 4)) is on the plane 5x + 7y – 6z = 0. а. || b. Show that the line Span((9,-3, 4)) is not on the plane 3x – 4y – 9z = 0. the line Span({(5,-2, 3)}) is с. d. Decide whether or not the plane on Span({( 1,-8,–7), (-2, 1, 4)}) Decide whether or not the line with symmetric equations: е. y 5 -3 is on the plane Span({{1, 3, 6), (–2, 1, 0)}).
Transcribed Image Text:14. Lines on a Plane in Space. Suppose that L is a line in Cartesian space, and II is a plane in Cartesian space. We will say that L is on II, or L c II if every point on L is also a point on II. This means that the coordinates of every point on L must satisfy the Cartesian equation of II. Show that the line with vector equation (x, y, z) = t(3, 5,–3) is on the plane 7x — Зу + 2z 3D 0. Show that the line Span({9,-3, 4)) is on the plane 5x + 7y – 6z = 0. а. || b. Show that the line Span((9,-3, 4)) is not on the plane 3x – 4y – 9z = 0. the line Span({(5,-2, 3)}) is с. d. Decide whether or not the plane on Span({( 1,-8,–7), (-2, 1, 4)}) Decide whether or not the line with symmetric equations: е. y 5 -3 is on the plane Span({{1, 3, 6), (–2, 1, 0)}).
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