a) Find an equation of the line through P(1,-2,4) with direction vector v=[2,4,-4] b) Find the equation of the plane containing the points A(2,1,1), B(0,4,1), and C(-2,1,4) c) Find the intersection of the line in a) and the plane in b)
a) Find an equation of the line through P(1,-2,4) with direction vector v=[2,4,-4] b) Find the equation of the plane containing the points A(2,1,1), B(0,4,1), and C(-2,1,4) c) Find the intersection of the line in a) and the plane in b)
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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for part c please, thank you!
![### Problem Set
**a) Find an equation of the line through \( P(1, -2, 4) \) with direction vector \( \mathbf{v} = [2, 4, -4] \)**
**b) Find the equation of the plane containing the points \( A(2, 1, 1) \), \( B(0, 4, 1) \), and \( C(-2, 1, 4) \)**
**c) Find the intersection of the line in (a) and the plane in (b)**](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6674a345-3819-404a-bb58-af4f58fff999%2Fbbf086a6-30cc-40b5-a922-af4b7cd16703%2Fm2y4jw5_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Problem Set
**a) Find an equation of the line through \( P(1, -2, 4) \) with direction vector \( \mathbf{v} = [2, 4, -4] \)**
**b) Find the equation of the plane containing the points \( A(2, 1, 1) \), \( B(0, 4, 1) \), and \( C(-2, 1, 4) \)**
**c) Find the intersection of the line in (a) and the plane in (b)**
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