1. Given a line P(t) through the points Po = [1,0|7 and P [2,4]7 in 2D(a) Extend P(t) to homogeneous coordinates(b) Compute the intersection of P(t) with the homogeneous plane 2 3h in homogeneouscOordinates(c) What is the point of intersection in non-homogeneons coordinates ?

The problem is concerned with projective plane , line and homogeneous coordinates

Answered: 1. Given a line P(t) through the points…

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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Find: The shortest distance from the point (2, 1, 3) to the plane x+y+z= 1. = The shortest distance between the line parametrized by (x, y, z) (4-t, 3+ t, −1+t) and the line parametrized by (x, y, z) = (4+ s, −1 – 2s, 1 — s). -
Let L be the line passing through the point P=(4, −3, 1) with direction vector =[−4, 1, 1]ª, and let T be the plane defined by 5x+4y—4z = 37. Find the point Q where L and T intersect. Q=(0, 0, 0)
4. What is the equation of the plane through (1,2,3) parallel to the plane x – 2y + 3z = 9? (a) x-2y + 3z + 3 = 0 (c) x- 2y + 3z + 6 = 0 (c) x - 2y + 3z – 6 = 0 (d) a, b, & c
Q3: Let L be the line of intersection of the planes 3x + y -z = 4 and 5x + y + 2z = 1 Find the plane equation that passes through L and the point A(1, 0, -1).
1. a) show that the lines [x, y, z] and x = y-7/-8=z-1/2 lie on the plane 2x + y + 3z - 10=0 b) find the point of intersection between these two lines.
a) Determine the equation of the line ℓ passing through the points (2, 1, 3) and (3, 2, 6). (0.2) b) Determine the intersection between ℓ and the line ℓ " : (x, y, z) = (−2 − t, 2 + t, 1 + t), t ∈ R. (0,4) c) Determine the intersection between ℓ and the plane π : 2x − 3y + z = 2.
Let L be the line passing through the point P(1, 2, −1) with direction vector d=[-2, −3, −4]T, and let T be the plane defined by −3x+5y-2z = −17. Find the point Q where L and T intersect. Q=(0,0,0)
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1. Given a line P(t) through the points Po = [1,0|7 and P [2,4]7 in 2D (a) Extend P(t) to homogeneous coordinates (b) Compute the intersection of P(t) with the homogeneous plane 2 3h in homogeneous cOordinates (c) What is the point of intersection in non-homogeneons coordinates ?