Answered: Find the vector form of the equation of…

Find the vector form of the equation of the plane that passes through the point P0 = (1, −2, 3) and has normal vector ~n =< 3, 1, −1 >.

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter4: Vector Spaces

Section4.4: Spanning Sets And Linear Independence

Problem 69E

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Concept explainers

Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.

Question

finding vector and equition of a line

(a) Find the vector form of the equation of the plane that passes through the point P0 = (1, −2, 3)

and has normal vector ~n =< 3, 1, −1 >.

(b) Find an equation for the plane that contains the line x = −1 + 3t, y = 5 + 3t, z = 2 + t and is

parallel to the line of intersection of the planes x −2(y −1) + 3z = −1 and y = −2x −1 = 0.

Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.

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