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Consider points P= (1, 2, 3) and Q = (-2, 3, a), where a € R is a parameter. Let S be the plane given by the equation 2x+3y-z = 4. . For a = 2, write in parametric form the line passing through P and Q. Hence or otherwise, show that the line intersects the plane S, and determine the point of intersection. Determine the value of a such that the line passing through P and Q does not intersect the plane S.

Consider points P= (1, 2, 3) and Q = (-2, 3, a), where a € R is a parameter. Let S be the plane given by the equation 2x+3y-z = 4. . For a = 2, write in parametric form the line passing through P and Q. Hence or otherwise, show that the line intersects the plane S, and determine the point of intersection. Determine the value of a such that the line passing through P and Q does not intersect the plane S.

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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H2) Consider points P = (1, 2, 3) and Q = (–2, 3, a), where a € R is a parameter. Let S be the plane given by the equation 2x + 3y – z = 4. a. For a = 2, write in parametric form the line passing through P and Q. Hence or otherwise, show that the line intersects the plane S, and determine the point of intersection. b. Determine the value of a such that the line passing through P and Q does not intersect the plane S.
Transcribed Image Text:H2) Consider points P = (1, 2, 3) and Q = (–2, 3, a), where a € R is a parameter. Let S be the plane given by the equation 2x + 3y – z = 4. a. For a = 2, write in parametric form the line passing through P and Q. Hence or otherwise, show that the line intersects the plane S, and determine the point of intersection. b. Determine the value of a such that the line passing through P and Q does not intersect the plane S.
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