Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
Suppose vector i = [-3,4,-6] and originates at point A at (1,5,-3) and terminates at point 8 at (3,6,9) a. Find vector and write it in both ordered pair and unit vector notation b. Find a normal to vectors and c. Find a unit vector that is the same magnitude as the normal you obtained in question 2, part b. d. Use the dot product to verify that the normal you obtained in question 2, part b is orthogonal to both vectors and e. Suppose vectors and are both direction vectors in a plane that also contains the point (2,-4,7). Determine: L A vector equation for the plane Parametric equations for the plane A scalar equation for the plane

Suppose vector i = [-3,4,-6] and originates at point A at (1,5,-3) and terminates at point 8 at (3,6,9) a. Find vector and write it in both ordered pair and unit vector notation b. Find a normal to vectors and c. Find a unit vector that is the same magnitude as the normal you obtained in question 2, part b. d. Use the dot product to verify that the normal you obtained in question 2, part b is orthogonal to both vectors and e. Suppose vectors and are both direction vectors in a plane that also contains the point (2,-4,7). Determine: L A vector equation for the plane Parametric equations for the plane A scalar equation for the plane

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter8: Applications Of Trigonometry
Section8.4: The Dot Product
Problem 48E
See similar textbooks
icon
Related questions
Question
Suppose vector i = [-3,4,-6) and originates at point A at (1,5,-3) and terminates at point B at (3,6,9) a. Find vector and write it in both ordered pair and unit vector notation b. Find a normal to vectors and c. Find a unit vector that is the same magnitude as the normal you obtained in question 2, part b. Use the dot product to verify that the normal you obtained in question 2, part b is orthogonal to both vectors and d. e. Suppose vectors i and are both direction vectors in a plane that also contains the point (2,-4,7). Determine: L A vector equation for the plane Parametric equations for the plane A scalar equation for the plane
Transcribed Image Text:Suppose vector i = [-3,4,-6) and originates at point A at (1,5,-3) and terminates at point B at (3,6,9) a. Find vector and write it in both ordered pair and unit vector notation b. Find a normal to vectors and c. Find a unit vector that is the same magnitude as the normal you obtained in question 2, part b. Use the dot product to verify that the normal you obtained in question 2, part b is orthogonal to both vectors and d. e. Suppose vectors i and are both direction vectors in a plane that also contains the point (2,-4,7). Determine: L A vector equation for the plane Parametric equations for the plane A scalar equation for the plane
QUESTION # 2: Cliven that, J = [-3, 4, -6] c) (ordered pair notation) [Using part 6) n U = 2₁ + Ĵ + 12k (unit vector notation) Verifying ʼn is orthogonal to t a) So, V = [2, 1, 12], J b) R² = √₂ x ✓ R= AI V = [ 3-1, 6-5, 9 +3] V = [2₁1, 12] F(x -3 4 K -6 2 1 121 R² = 1 (48 + 6) - √(-36 +12) + ^(-3-8) 7² = 54₁ +249-11 R to Let = (54, 24, -117 J (54) ² + (24)² + (-11)² = 254, 24, -117 √2916 +376 + 121 =<54, 24, -117 33613 03613 (441249-11K) ñ·ū = [54, 24, -11], [-3, 4, -6] = -162 +96 +66 = 0 Verifying in is orthogonal to n⋅V = CS4, 24, -11]. [2, 1, 12] = 105 + 24 - 132 e) Planc contains (2, +4,7) normal (n) = [$4, 24, -11] Vector Equation [R-(21-43₁.7K)]. [54₁ +245-11k] = 0 = Pargmetric, equation U= [-3₁4₁-6] V= [211, 12] x=2-3£1+ 2+2 y = = 4 +4€2+€₂ 2-7 -6€₁ + 12 € ₂ Scolar Equation 54(x-2) ₁24 (y + 4) - 11 (2-7)=0 54x + 24y - 112 + 65 =6
Transcribed Image Text:QUESTION # 2: Cliven that, J = [-3, 4, -6] c) (ordered pair notation) [Using part 6) n U = 2₁ + Ĵ + 12k (unit vector notation) Verifying ʼn is orthogonal to t a) So, V = [2, 1, 12], J b) R² = √₂ x ✓ R= AI V = [ 3-1, 6-5, 9 +3] V = [2₁1, 12] F(x -3 4 K -6 2 1 121 R² = 1 (48 + 6) - √(-36 +12) + ^(-3-8) 7² = 54₁ +249-11 R to Let = (54, 24, -117 J (54) ² + (24)² + (-11)² = 254, 24, -117 √2916 +376 + 121 =<54, 24, -117 33613 03613 (441249-11K) ñ·ū = [54, 24, -11], [-3, 4, -6] = -162 +96 +66 = 0 Verifying in is orthogonal to n⋅V = CS4, 24, -11]. [2, 1, 12] = 105 + 24 - 132 e) Planc contains (2, +4,7) normal (n) = [$4, 24, -11] Vector Equation [R-(21-43₁.7K)]. [54₁ +245-11k] = 0 = Pargmetric, equation U= [-3₁4₁-6] V= [211, 12] x=2-3£1+ 2+2 y = = 4 +4€2+€₂ 2-7 -6€₁ + 12 € ₂ Scolar Equation 54(x-2) ₁24 (y + 4) - 11 (2-7)=0 54x + 24y - 112 + 65 =6
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 5 steps with 21 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
Algebra
ISBN:
9781305658004
Author:
Ron Larson
Publisher:
Cengage Learning
Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Trigonometry (MindTap Course List)
Trigonometry (MindTap Course List)
Trigonometry
ISBN:
9781305652224
Author:
Charles P. McKeague, Mark D. Turner
Publisher:
Cengage Learning
SEE MORE TEXTBOOKS