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2. A triangle is formed by the points P = (1,0, 3), Q=(4,-1, 3), and R = (6, 1, -2). (a) Sketch the triangle. (b) Find the vector and scalar equations of the plane containing this triangle. (6) Vector Equati

2. A triangle is formed by the points P = (1,0, 3), Q=(4,-1, 3), and R = (6, 1, -2). (a) Sketch the triangle. (b) Find the vector and scalar equations of the plane containing this triangle. (6) Vector Equati

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter8: Applications Of Trigonometry
Section8.3: Vectors
Problem 11E
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2. A triangle is formed by the points P = (1,0,3), Q =(4,-1,3), and R = (6,1,-2). (a) Sketch the triangle. (b) Find the vector and scalar equations of the plane containing this triangle. (a), PQ = (4-1, 1-0, 3-3) 3 PR= (6-1, 1-0, -2-3) (5, 1,-5) (a) z P Answer for (b): ana →y (6) Vector Equation: 8 = (1, 0, 3) + + PO tờ Sp 7 = (1,0, 3) + t (3,-1,0) + s (5,1,-5) 7 = (1+3+ + 55,₁ - t+s, 3-5s) Scalar Equation: di 2-3 X-1 4-1 у-о -1-0 X-1 3 + SPRI 6-1 1-0-2-3 1-2- 9 -1 3-3 z-3 O = 0 =0 5 ) -5 (x-1) (5-0) -y (-15-0) + (2-3) (3+5) = 0 5x -5 +15y + 8z - 24 = 0 5x +15y +8² = 29 Vector Equation: 7 = (1+3+ +5s, -t+s, 3-5s) Scalar Equation : 5x+15y + 8z = 29
Transcribed Image Text:2. A triangle is formed by the points P = (1,0,3), Q =(4,-1,3), and R = (6,1,-2). (a) Sketch the triangle. (b) Find the vector and scalar equations of the plane containing this triangle. (a), PQ = (4-1, 1-0, 3-3) 3 PR= (6-1, 1-0, -2-3) (5, 1,-5) (a) z P Answer for (b): ana →y (6) Vector Equation: 8 = (1, 0, 3) + + PO tờ Sp 7 = (1,0, 3) + t (3,-1,0) + s (5,1,-5) 7 = (1+3+ + 55,₁ - t+s, 3-5s) Scalar Equation: di 2-3 X-1 4-1 у-о -1-0 X-1 3 + SPRI 6-1 1-0-2-3 1-2- 9 -1 3-3 z-3 O = 0 =0 5 ) -5 (x-1) (5-0) -y (-15-0) + (2-3) (3+5) = 0 5x -5 +15y + 8z - 24 = 0 5x +15y +8² = 29 Vector Equation: 7 = (1+3+ +5s, -t+s, 3-5s) Scalar Equation : 5x+15y + 8z = 29
PO and = 3. Recall points P, Q, and R from Question 2. Suppose I have a fourth point S (5,3,2). Using vectors v = PŘ, determine: W = (a) The area of the parallelogram formed by vectors v an w. (b) The volume of the parallelepiped formed by incorporating the point S.
Transcribed Image Text:PO and = 3. Recall points P, Q, and R from Question 2. Suppose I have a fourth point S (5,3,2). Using vectors v = PŘ, determine: W = (a) The area of the parallelogram formed by vectors v an w. (b) The volume of the parallelepiped formed by incorporating the point S.
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