Welcome :: Homework Help and Answers :: Mathskey.com
Welcome to Mathskey.com Question & Answers Community. Ask any math/science homework question and receive answers from other members of the community.

13,435 questions

17,804 answers

1,438 comments

339,689 users

Grade 12 Vectors help please, intersection of planes?

0 votes

For what value of k will the following set of planes intersect in a line?

x-2y-z=0
x+9y-5z=0
kx-y+z=0


I have to solve this using matrices. Thank you

asked Jun 12, 2013 in PRECALCULUS by chrisgirl Apprentice

2 Answers

0 votes

Given equations are x-2y-z=0

                                 x+9y-5z=0

                                 kx-y+z=0

The above equations can be written in matrix form as

image

R2 -> R2 - R1

image

image

R1 -> 11R1 + 2R2

image

image

R1 -> R1/11 and R2 -> R2/11

image

R3 -> R3 + R2

image

image

R3 -> R3 - KR1

image

image

In order to have a unique solution (without parameters), we need toequalise the bottom right corner to 1. We get,

                      7/11+(19/11)k=1

                      (19/11)k=1-(7/11)

                      (19/11)k=4/11

                     19k=4

                      k=4/19

Therefore the value of k is 4/11.

      

answered Jun 14, 2013 by joly Scholar
reshown Jun 23, 2013 by moderator
0 votes

Rule for planes intersect in a line is Rank of the matrices is 2

x-2y-z=0
x+9y-5z=0
kx-y+z=0

Rank 2 means determent is zero.

image

answered Jun 15, 2013 by bradely Mentor

Related questions

asked Feb 13, 2015 in CALCULUS by anonymous
asked Jul 25, 2014 in TRIGONOMETRY by anonymous
...