Consider the equation in x, y, z: : y² + z² = 1, x = [0, 2], y ≥ 0, z ≥ 0 Note the domain conditions for Q. Note: Q2 = {(x, y, z)| y² + z² = 1 and x = [0, 2] and y ≥ 0 and z ≥ 0} Ω a) Sketch the cross section of 2 by the plane O₁: x = 1 b) Sketch the cross section of 2 by the plane O2: y = 1 c) SKETCH Q

Q: The plane 7= [1,0,0]+t[1,1,1]+s[L,−1,1]; s,t €R contains the point (3,0, p). Find the value of p.

A: Given r=(1,0,0)+t(1,1,1)+s(1,-1,1)

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Q: Find a plane through P (2, 1, 1) and perpendicular to the line of intersec- tion of the planes:…

A: find a plane through P2,1,1 and perpendicular to the line of intersection of the planes  2x+y-z=3 ,…

Q: What is the parametric equation for the line of intersection of the planes x + y - z = 2 and 3x - 4y…

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Q: 4. (a) Show that the line l given by l: 1= 2+3t, y=1+4t, z= 5+ 2t, te R, lies in the plane II given…

A: Given problem:- Show that the line  given by   l : x = 2 + 3t , y = 1 + 4t , z=5+2t ,t in R   lies…

Q: 2. Determine the value of ß such that the distance between the plane \pi and the line r is constant,…

A: I have appended the formula used in solution procedure

Q: Find the value of k so that the line [x, y, z] = [2, -2, 0] + t[3, 5, k] is parallel to the plane 4x…

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Q: What angle does the line of interaction of the planes 2x+y-z = 0 and x+y+2z= 0 make with the…

A: The direction vector of the line of the interaction of the two planes is equal to the cross product…

Q: Find the point of intersection of the line l: x = 2+ 3t, y = 1 – 6t, z = 4 – 2t with the plane - 2x…

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Q: Find the distance between the line 2x - 3y + z = 6, 2y- z = 4, and the plane passing through the…

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Q: ) find the eq. Plane that Contains the -=9+ 6 = 2 - X-y= 2-4 and Passes through origin? %3D…

A: Equation of any plane passing through origin is  ax+by+c=0 And follow step 2nd  .

Q: (b) Let A(4,4, 7) and B(11,8, 11) be two points in 3D. Determine the coordinates of the point Q…

A: Introduction: When a vector is a non-zero scalar multiple of another vector, the two vectors are…

Q: 1. Determine the point of intersection between the line, L: x = 3+t, y=4-5t, z=1-7t, te R, and the…

A: As per rule of bartleby we can solve only one question at a time and we can solve only three subpart…

Q: A line has parametric eauation s: x = 8 – 21, y = -9 + 3t, z = 6 – t At what time does the line…

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Q: b) Find the equation of the plane containing lines ₁ : x = 2+5t, y = 4+2t, z = -t and l₂: x=2-t₁y =…

A: We have to find the equation of the plane containing lines l1 : x=2+5t, y=4+2t, z=-t and l2 : x=2-t,…

Q: Ex: Find egns of the line thru the pt ( -!,), perpendicular bo the line 3x= 2y == and paralled to…

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Q: a) Check that the line r: (x, y, z) = (1,0,1) + t(1, –1,0) is parallel to the plane n:x + y +z = 0;…

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