Discrete Mathematics 12

In summary, the scalar equation of the plane that is perpendicular to the plane with normal vector [3,1,2] and passes through points A(2,-6,-1) and B(1,2,-4) can be found by taking the cross product of [3,1,2] and [1,-4,-3] to get the direction vector of the new plane.
  • #1
eme_girl
5
0
Find the scalar eq'n of a plane that is perpendicular to the plane with normal vector [3,1,2] and passes through points A(2,-6,-1) and B(1,2,-4).

I think that the normal vector can be the direction vector of this new plane. But then, in order to find the scalar eq'n I need a normal vector of this new plane. How do I find this?
 
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  • #2
Strictly speaking a plane doesn't have a "direction vector". What is true is that the vector [3,1,2] is in the plane you want. You also know that the vector from A(2,6,-1) to B(1,2,-4) (which is, of course, [1-2,2-6,-4-(-1)]= [-1, -4, -3] is in the plane. Do you know how to find a vector that is perpendicular to both [3,1,2] and [1,4,-3]?
 
  • #3
I understand what you just found. But no, I do not know how to find a vector's that perpendicular to both those vectors.
 
  • #4
eme_girl,
do u know the direction of a vector that is a cross product of two vectors?

-- AI
 
  • #5
TenaliRaman's point: the cross product of two vectors is always perpendicular to both.

The cross product of [a1,a2,a3] and [b1,b2,b3] is the vector [a2b3-a3b2,a3b1-a1b3,a1b2-a2b1].
 

What is Discrete Mathematics 12?

Discrete Mathematics 12 is a branch of mathematics that deals with mathematical structures and objects that are countable or distinct in nature. It includes topics such as logic, set theory, graph theory, combinatorics, and algorithms.

What are the applications of Discrete Mathematics 12?

Discrete Mathematics 12 has a wide range of applications in various fields such as computer science, engineering, finance, and cryptography. It is used for solving real-world problems involving decision-making, optimization, and data analysis.

What are the key concepts in Discrete Mathematics 12?

Some of the key concepts in Discrete Mathematics 12 include propositional logic, predicate logic, sets and functions, graph theory, combinatorics, and algorithms. These concepts form the foundation for more advanced topics in the field.

How is Discrete Mathematics 12 different from other branches of mathematics?

Discrete Mathematics 12 is different from other branches of mathematics, such as calculus and algebra, because it deals with objects that are countable and finite, rather than continuous and infinite. It also focuses on discrete structures and algorithms, rather than continuous functions and equations.

What skills are needed to study Discrete Mathematics 12?

To study Discrete Mathematics 12, one should have a strong foundation in algebra and logic. It also requires critical thinking, problem-solving, and analytical skills. Basic computer programming skills are also beneficial as many topics in Discrete Mathematics 12 have applications in computer science.

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