Explanation Given: The equation of a plane n ⋅ 〈 x , y , z 〉 = d is said to be in normal form if n is a unit vector . Formula used: The orthogonal distance D from the plane P , with the equation a x + b y + c z + d = 0 to the origin O is D = | d | a 2 + b 2 + c 2 . Calculation: Consider the equation of a plane n ⋅ 〈 x , y , z 〉 = d in normal form if n is a unit vector. We can rewrite it as: n ⋅ 〈 x , y , z 〉 − d = 0 The orthogonal distance with the equation a x + b y + c z + d = 0 to the origin O is D = | d | a 2 + b 2 + c 2 = | d | ‖ n ‖ It is given that n is a unit vector, so ‖ n ‖ = 1 . Thus, the orthogonal distance of the plane from the origin O is D = | d | ...

3rd Edition

ISBN: 9781464125263

Author: Jon Rogawski, Colin Adams

Publisher: W.H. Freeman & Co

See similar textbooks

Videos

Question

Chapter 13.5, Problem 78E

To determine

Show that $| d |$ is the distance from the plane to origin. Write the equation of the plane $4 x - 2 y + 4 z = 24$ in normal form.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 13.5, Problem 77E

Chapter 13.6, Problem 1PQ

Students have asked these similar questions

3. Consider the sequences of functions f₁: [-π, π] → R, sin(n²x) An(2) n f pointwise as (i) Find a function ƒ : [-T,π] → R such that fn n∞. Further, show that fn →f uniformly on [-π,π] as n → ∞. [20 Marks] (ii) Does the sequence of derivatives f(x) has a pointwise limit on [-7, 7]? Justify your answer. [10 Marks]

1. (i) Give the definition of a metric on a set X. [5 Marks] (ii) Let X = {a, b, c} and let a function d : XxX → [0, ∞) be defined as d(a, a) = d(b,b) = d(c, c) 0, d(a, c) = d(c, a) 1, d(a, b) = d(b, a) = 4, d(b, c) = d(c,b) = 2. Decide whether d is a metric on X. Justify your answer. = (iii) Consider a metric space (R, d.), where = [10 Marks] 0 if x = y, d* (x, y) 5 if xy. In the metric space (R, d*), describe: (a) open ball B2(0) of radius 2 centred at 0; (b) closed ball B5(0) of radius 5 centred at 0; (c) sphere S10 (0) of radius 10 centred at 0. [5 Marks] [5 Marks] [5 Marks]

(c) sphere S10 (0) of radius 10 centred at 0. [5 Marks] 2. Let C([a, b]) be the metric space of continuous functions on the interval [a, b] with the metric doo (f,g) = max f(x)g(x)|. xЄ[a,b] = 1x. Find: Let f(x) = 1 - x² and g(x): (i) do(f, g) in C'([0, 1]); (ii) do(f,g) in C([−1, 1]). [20 Marks] [20 Marks]

Chapter 13 Solutions

Calculus - Standalone book

Ch. 13.1 - Prob. 1PQ Ch. 13.1 - Prob. 2PQ Ch. 13.1 - Prob. 3PQ Ch. 13.1 - Prob. 4PQ Ch. 13.1 - Prob. 5PQ Ch. 13.1 - Prob. 6PQ Ch. 13.1 - Prob. 1E Ch. 13.1 - Prob. 2E Ch. 13.1 - Prob. 3E Ch. 13.1 - Prob. 4E

Knowledge Booster

$Calculus$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.

Show that | d | is the distance from the plane to origin. Write the equation of the plane 4 x − 2 y + 4 z = 24 in normal form.

Solution Summary: The author explains that the orthogonal distance of the plane from the origin O is D = | d |.

Videos

Show that $| d |$ is the distance from the plane to origin. Write the equation of the plane $4 x - 2 y + 4 z = 24$ in normal form.

Want to see the full answer?

Chapter 13 Solutions

Show that | d | is the distance from the plane to origin. Write the equation of the plane 4 x − 2 y + 4 z = 24 in normal form.

Solution Summary: The author explains that the orthogonal distance of the plane from the origin O is D = | d |.

Videos

Show that |d| is the distance from the plane to origin. Write the equation of the plane 4x−2y+4z=24 in normal form.

Want to see the full answer?

Chapter 13 Solutions

Show that $| d |$ is the distance from the plane to origin. Write the equation of the plane $4 x - 2 y + 4 z = 24$ in normal form.