Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN: 9781285741550
Author: James Stewart
Publisher: Cengage Learning
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**Part 1 of 4** A triangle \( \triangle PQR \) has vertices \( P(2, -2, 1) \), \( Q(1, -3, -1) \), \( R(-2, 2, 1) \). *Use the distance formula to determine the length, \( |QR| \), of the side \( QR \) of the triangle.* 1. \( |QR| = \sqrt{39} \) 2. \( |QR| = 2\sqrt{10} \) 3. \( |QR| = \sqrt{38} \) 4. \( |QR| = \sqrt{41} \) 5. \( |QR| = \sqrt{37} \) --- **Part 2 of 4** A triangle \( \triangle PQR \) has vertices \( P(-1, 2, -1) \), \( Q(-2, 2, 1) \), \( R(0, 4, 1) \). *Use the distance formula to decide which one of the following properties the triangle has.* 1. Isosceles with \( |QP| = |QR| \) 2. Not isosceles 3. Isosceles with \( |PQ| = |PR| \) 4. Isosceles with \( |RP| = |RQ| \) --- **Part 3 of 4** *Find an equation for the sphere having center at (2, 3, 2) and radius 3.* 1. \( 2x^2 + 3y^2 + 2z^2 = 9 \) 2. \( x^2 + y^2 + z^2 - 4x - 6y - 4z = 8 \) 3. \( 2x^2 + 3y^2 + 2z^2 + 9 = 0 \) 4. \( x^2 + y^2 + z^2 + 4x + 6y + 4z = 8 \) 5. \( x^2 + y^2 + z^2 - 4x - 6y - 4z + 8 = 0 \) 6. \( x^2 + y^2 + z^2 + 4x + 6y + 4z
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Transcribed Image Text:**Part 1 of 4** A triangle \( \triangle PQR \) has vertices \( P(2, -2, 1) \), \( Q(1, -3, -1) \), \( R(-2, 2, 1) \). *Use the distance formula to determine the length, \( |QR| \), of the side \( QR \) of the triangle.* 1. \( |QR| = \sqrt{39} \) 2. \( |QR| = 2\sqrt{10} \) 3. \( |QR| = \sqrt{38} \) 4. \( |QR| = \sqrt{41} \) 5. \( |QR| = \sqrt{37} \) --- **Part 2 of 4** A triangle \( \triangle PQR \) has vertices \( P(-1, 2, -1) \), \( Q(-2, 2, 1) \), \( R(0, 4, 1) \). *Use the distance formula to decide which one of the following properties the triangle has.* 1. Isosceles with \( |QP| = |QR| \) 2. Not isosceles 3. Isosceles with \( |PQ| = |PR| \) 4. Isosceles with \( |RP| = |RQ| \) --- **Part 3 of 4** *Find an equation for the sphere having center at (2, 3, 2) and radius 3.* 1. \( 2x^2 + 3y^2 + 2z^2 = 9 \) 2. \( x^2 + y^2 + z^2 - 4x - 6y - 4z = 8 \) 3. \( 2x^2 + 3y^2 + 2z^2 + 9 = 0 \) 4. \( x^2 + y^2 + z^2 + 4x + 6y + 4z = 8 \) 5. \( x^2 + y^2 + z^2 - 4x - 6y - 4z + 8 = 0 \) 6. \( x^2 + y^2 + z^2 + 4x + 6y + 4z
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