Question

If $l(a, b, c)=\sqrt{a^{2}+b^{2}+c^{2}},$ find: (a) $l(5,3,2)$ (b) $l(3,0,4)$ (c) $l(x, y, z)$

Name: Problem 45, Chapter 0: Calculus
Uploaded: 2022-02-06T01:00:44-08:00
Duration: 1 min
Channel: Raj Bala
Description: If l(a, b, c)=√(a^2+b^2+c^2), find: (a) l(5,3,2) (b) l(3,0,4) (c) l(x, y, z)

   If $l(a, b, c)=\sqrt{a^{2}+b^{2}+c^{2}},$ find:
(a) $l(5,3,2)$
(b) $l(3,0,4)$
(c) $l(x, y, z)$

Calculus

Laura Taalman, Peter… 1st Edition

Chapter 0, Problem 45

Instant Answer

Solved by Expert Raj Bala

02/06/2022

Step 1

We need to find the value of this function for different sets of values for $a$, $b$, and $c$. Show more…

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If $l(a, b, c)=\sqrt{a^{2}+b^{2}+c^{2}},$ find: (a) $l(5,3,2)$ (b) $l(3,0,4)$ (c) $l(x, y, z)$

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Key Concepts

Euclidean Norm

The Euclidean norm is a measure of the magnitude or length of a vector in Euclidean space. It is defined as the square root of the sum of the squares of the vector's components. This concept is fundamental in linear algebra and geometry, as it extends the Pythagorean theorem to higher dimensions, allowing us to compute distances and magnitudes in spaces beyond the ordinary two-dimensional plane.

Substitution and Function Evaluation

Substitution is the process of replacing variables in an expression or function with specific values to simplify the calculation or evaluation. In the context of the Euclidean norm, this means substituting the given components of a vector into the formula to determine its magnitude. This key concept underlies many areas of mathematics, enabling the application of formulas to solve specific problems.

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