How Can We Geometrically Describe Vectors Orthogonal to the Vector $(-4,1,-3)$?

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In summary, geometrical description is a method of using mathematical concepts and principles to describe and analyze the physical properties and relationships of objects in space. There are three main types of geometrical description - Euclidean, Non-Euclidean, and Analytic geometry - each with its own focus and applications. It has practical uses in various fields such as architecture, engineering, and navigation, and is based on fundamental elements like points, lines, angles, planes, and solids. Understanding geometrical description requires a strong understanding of math, critical thinking, and visual-spatial skills.
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mathmari
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Hey!

How could we describe geometrically the vectors that are orthogonal to the Vector $(-4,1,-3)$ ?
 
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mathmari said:
Hey!

How could we describe geometrically the vectors that are orthogonal to the Vector $(-4,1,-3)$ ?

Hey mathmari! (Smile)

It's the plane perpendicular to the vector that contains the origin.
Its equation is:
$$(x,y,z)\cdot (-4,1,-3)=0 \quad \Leftrightarrow \quad -4x+y-3z=0$$
(Mmm)
 
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Thank you very much! (Mmm)
 

FAQ: How Can We Geometrically Describe Vectors Orthogonal to the Vector $(-4,1,-3)$?

What is geometrical description?

Geometrical description is a method of describing and analyzing the physical properties and relationships of objects in space using mathematical concepts and principles.

What are the different types of geometrical description?

The three main types of geometrical description are Euclidean geometry, Non-Euclidean geometry, and Analytic geometry. Euclidean geometry deals with flat, two-dimensional shapes and is the most commonly used type. Non-Euclidean geometry explores curved surfaces and three-dimensional space. Analytic geometry uses algebraic equations to represent geometrical shapes and their properties.

How is geometrical description used in real life?

Geometrical description has many practical applications in daily life. It is used in fields such as architecture, engineering, and design to create accurate and precise plans and models. It is also used in navigation and mapping, as well as in computer graphics and animation.

What are the fundamental elements of geometrical description?

The fundamental elements of geometrical description include points, lines, angles, planes, and solids. These elements are used to define and describe the characteristics and relationships of geometrical objects.

What skills are required for understanding geometrical description?

To understand geometrical description, one needs to have a strong grasp of mathematical concepts, such as algebra and geometry. It also requires critical thinking and visual-spatial skills to visualize and manipulate geometrical objects in different dimensions.

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