Explanation Given: A plane intersects to the respective axes and forms the Intercepts over the x axis is ( a , 0 , 0 ) , y axis is ( 0 , b , 0 ) , z axis is ( 0 , 0 , c ) . Approach: Using vector algebra to solve for the query, such that equation of the plane is to be determined as n ^ ⋅ ( X − A ) = 0 . Calculation: Intercepts over the x axis is ( a , 0, 0), y axis is ( 0, b , 0), z axis is (0, 0, c). Such that basis over the respective coordinate axes will be A = [ a 0 0 ] B = [ 0 b 0 ] C = [ 0 0 c ] Let’s find out normal over the plane Which can be find out as n ^ = A B → × A C → A B → = [ 0 b 0 ] − [ a 0 0 ] = [ − a b 0 ] A C → = [ o o c ] − [ a 0 0 ] = [ − a o c ] And n ^ = A B → × A C → = [ − a b 0 ] × [ − a 0 c ] Which can be calculated as

Introduction to Linear Algebra (Classic Version) (5th Edition) (Pearson Modern Classics for Advanced Mathematics Series)

5th Edition

ISBN: 9780134689531

Author: Lee Johnson, Dean Riess, Jimmy Arnold

Publisher: PEARSON

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Chapter 2.SE, Problem 10SE

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A plane intersects the axes at points of x(a,0,0), y(0,b,0) and z(0,0,c), find the equation of the plane and express that in form of αx+βy+χz=1.

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Chapter 2.SE, Problem 9SE

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Chapter 2 Solutions

Introduction to Linear Algebra (Classic Version) (5th Edition) (Pearson Modern Classics for Advanced Mathematics Series)

Ch. 2.1 - In Exercises 1-4, graph the geometric vector u=AB...Ch. 2.1 - Prob. 2E Ch. 2.1 - Prob. 3E Ch. 2.1 - Prob. 4E Ch. 2.1 - Let u=AB and v=CD where...Ch. 2.1 - In Exercises 6-9, find the unspecified coordinates...Ch. 2.1 - In Exercises 6-9, find the unspecified coordinates...Ch. 2.1 - In Exercises 6-9, find the unspecified coordinates...Ch. 2.1 - Prob. 9E Ch. 2.1 - Prob. 10E

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A plane intersects the axes at points of x ( a , 0 , 0 ) , y ( 0 , b , 0 ) and z ( 0 , 0 , c ) , find the equation of the plane and express that in form of α x + β y + χ z = 1 .

Solution Summary: The author explains how a plane intersects the axes at points of x, y, and c.

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To find:

A plane intersects the axes at points of x(a,0,0), y(0,b,0) and z(0,0,c), find the equation of the plane and express that in form of αx+βy+χz=1.

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Chapter 2 Solutions

A plane intersects the axes at points of x ( a , 0 , 0 ) , y ( 0 , b , 0 ) and z ( 0 , 0 , c ) , find the equation of the plane and express that in form of α x + β y + χ z = 1 .

Solution Summary: The author explains how a plane intersects the axes at points of x, y, and c.

Concept explainers

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To find: A plane intersects the axes at points of x(a,0,0), y(0,b,0) and z(0,0,c), find the equation of the plane and express that in form of αx+βy+χz=1.

Want to see the full answer?

Chapter 2 Solutions

To find:

A plane intersects the axes at points of x(a,0,0), y(0,b,0) and z(0,0,c), find the equation of the plane and express that in form of αx+βy+χz=1.