Consider the planes P₁: ax + by + cz = d₂ and P₂: ax + cy + bz = d₂ in R³, where a = 13, b = 52, c = 143, d₁ = 78 and d₂ = 260. a) Let n₁ = (p,q,r) be a normal for P₁. Suppose that r=22. State values for p and q. We have p= and q= b) Let P(x,y,z) be the point on P₂ with y = 2 and z = 0. State the value for x. We have x= c) Let u = (1,m,n) and v = (XYZ) be two vectors in R³, and let L: r=ut + v, for t in R, be the intersection of P₁ and P₂. Suppose that n=13 and z=0. State values for l, m, x, and yo and yo We have /= m=
Consider the planes P₁: ax + by + cz = d₂ and P₂: ax + cy + bz = d₂ in R³, where a = 13, b = 52, c = 143, d₁ = 78 and d₂ = 260. a) Let n₁ = (p,q,r) be a normal for P₁. Suppose that r=22. State values for p and q. We have p= and q= b) Let P(x,y,z) be the point on P₂ with y = 2 and z = 0. State the value for x. We have x= c) Let u = (1,m,n) and v = (XYZ) be two vectors in R³, and let L: r=ut + v, for t in R, be the intersection of P₁ and P₂. Suppose that n=13 and z=0. State values for l, m, x, and yo and yo We have /= m=
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![Consider
the planes P₁: ax + by + cz =d₁ and P₂: ax + cy + bz = d₂ in R³, where a = 13, b = 52, c = 143, d₂ = 78 and d₂ = 260.
a) Let n₁ = (p,q,r) be a normal for P₁. Suppose that r=22. State values for p and q.
We have p=
and q=
].
b) Let P(x,y,z) be the point on P₂ with y = 2 and z = 0. State the value for x.
We have x=
c) Let u = (1,m,n) and v = (X,Y,Z) be two vectors in R³, and let L: r=ut + v, fort in R, be the intersection of P₁ and P₂. Suppose that n=13 and zo=0. State values for l, m, x, and yo
, and yo
, xo=1
We have /=
m=](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F76a38be8-a1f5-46f2-a405-6a748a1c86fe%2F720e4efd-3da1-4d66-bd3c-f2983aa8431d%2Fe1d62we_processed.png&w=3840&q=75)
Transcribed Image Text:Consider
the planes P₁: ax + by + cz =d₁ and P₂: ax + cy + bz = d₂ in R³, where a = 13, b = 52, c = 143, d₂ = 78 and d₂ = 260.
a) Let n₁ = (p,q,r) be a normal for P₁. Suppose that r=22. State values for p and q.
We have p=
and q=
].
b) Let P(x,y,z) be the point on P₂ with y = 2 and z = 0. State the value for x.
We have x=
c) Let u = (1,m,n) and v = (X,Y,Z) be two vectors in R³, and let L: r=ut + v, fort in R, be the intersection of P₁ and P₂. Suppose that n=13 and zo=0. State values for l, m, x, and yo
, and yo
, xo=1
We have /=
m=
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