5. Let II be the plane with equation x+y+z= 3, and let II₂ be the plane with equation 3x + 4y + z = 1. (a) Find two distinct vectors normal to II, and one vector normal to II₂. (b) Find a parametric equation of a line which is at right angles to II₁. (c) Find the angle in radians between the planes II and II₂, correct to two decimal places.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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5. Let II be the plane with equation x+y+z= 3, and let II₂ be the plane with equation
3x + 4y + z = 1.
(a) Find two distinct vectors normal to II, and one vector normal to II₂.
(b) Find a parametric equation of a line which is at right angles to II₁.
(c) Find the angle in radians between the planes II and II2, correct to two decimal
places.
Let c ER, and let L be the line with parametric equation
(x, y, z)= (1,0,0) + t(1, 2, c),
teR.
(d) Find the point of intersection of II₁ and L in the case c = -1.
(e) Find a value of c for which II, and I do not intersect.
Transcribed Image Text:5. Let II be the plane with equation x+y+z= 3, and let II₂ be the plane with equation 3x + 4y + z = 1. (a) Find two distinct vectors normal to II, and one vector normal to II₂. (b) Find a parametric equation of a line which is at right angles to II₁. (c) Find the angle in radians between the planes II and II2, correct to two decimal places. Let c ER, and let L be the line with parametric equation (x, y, z)= (1,0,0) + t(1, 2, c), teR. (d) Find the point of intersection of II₁ and L in the case c = -1. (e) Find a value of c for which II, and I do not intersect.
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