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Problem 1.1 Find the angles and the sides of the triangle determined by the points: P(1, 2, 3), (3, 1, -2), P(2, -3, -1) Problem 1.2 Find the intersecting point of the plane through the points: P(1,-1,1), P₂(3,-2,-1), P(1, 0, -2) and the line through the points: P₁(1,2,1), P₁(3, − 2, 2) . Problem 1.3 Find the volume of the tetrahedron determined by the points: P(1,2,1), P(3, 2, 2), P(2, 3, −1), P₁(2, 1, −1) Problem 1.4 Find the parametric equation of the line that is the intersection of the two planes: x+2y-3z = 4 and z = 2x-3y-1. Problem 1.5 Find the standard form of the equation of the plane determined by the parametric equation: x(s,t)=3-2s+t, y(s,t)=2+s−2, z(s,t)=1+2s+2 Problem 1.6 For the three vectors ā = (1,1,1), 5 =(−1,0,1), ĉ = (2,−1,-2) find two vectors x and y, such that: =x+, is in the plane determined by a and b, and y is perpendicular to this plane.

Problem 1.1 Find the angles and the sides of the triangle determined by the points: P(1, 2, 3), (3, 1, -2), P(2, -3, -1) Problem 1.2 Find the intersecting point of the plane through the points: P(1,-1,1), P₂(3,-2,-1), P(1, 0, -2) and the line through the points: P₁(1,2,1), P₁(3, − 2, 2) . Problem 1.3 Find the volume of the tetrahedron determined by the points: P(1,2,1), P(3, 2, 2), P(2, 3, −1), P₁(2, 1, −1) Problem 1.4 Find the parametric equation of the line that is the intersection of the two planes: x+2y-3z = 4 and z = 2x-3y-1. Problem 1.5 Find the standard form of the equation of the plane determined by the parametric equation: x(s,t)=3-2s+t, y(s,t)=2+s−2, z(s,t)=1+2s+2 Problem 1.6 For the three vectors ā = (1,1,1), 5 =(−1,0,1), ĉ = (2,−1,-2) find two vectors x and y, such that: =x+, is in the plane determined by a and b, and y is perpendicular to this plane.

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Problem 1.1 Find the angles and the sides of the triangle determined by the points: P(1, 2, 3), (3, 1, -2), P(2, -3, -1) Problem 1.2 Find the intersecting point of the plane through the points: P(1,-1,1), P₂(3,-2,-1), P(1, 0, -2) and the line through the points: P₁(1,2,1), P₁(3, − 2, 2) . Problem 1.3 Find the volume of the tetrahedron determined by the points: P(1,2,1), P(3, 2, 2), P(2, 3, −1), P₁(2, 1, −1) Problem 1.4 Find the parametric equation of the line that is the intersection of the two planes: x+2y-3z = 4 and z = 2x-3y-1. Problem 1.5 Find the standard form of the equation of the plane determined by the parametric equation: x(s,t)=3-2s+t, y(s,t)=2+s−2, z(s,t)=1+2s+2 Problem 1.6 For the three vectors ā = (1,1,1), 5 =(−1,0,1), ĉ = (2,−1,-2) find two vectors x and y, such that: =x+, is in the plane determined by a and b, and y is perpendicular to this plane.
Transcribed Image Text:Problem 1.1 Find the angles and the sides of the triangle determined by the points: P(1, 2, 3), (3, 1, -2), P(2, -3, -1) Problem 1.2 Find the intersecting point of the plane through the points: P(1,-1,1), P₂(3,-2,-1), P(1, 0, -2) and the line through the points: P₁(1,2,1), P₁(3, − 2, 2) . Problem 1.3 Find the volume of the tetrahedron determined by the points: P(1,2,1), P(3, 2, 2), P(2, 3, −1), P₁(2, 1, −1) Problem 1.4 Find the parametric equation of the line that is the intersection of the two planes: x+2y-3z = 4 and z = 2x-3y-1. Problem 1.5 Find the standard form of the equation of the plane determined by the parametric equation: x(s,t)=3-2s+t, y(s,t)=2+s−2, z(s,t)=1+2s+2 Problem 1.6 For the three vectors ā = (1,1,1), 5 =(−1,0,1), ĉ = (2,−1,-2) find two vectors x and y, such that: =x+, is in the plane determined by a and b, and y is perpendicular to this plane.
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