Question

Grade 12 vectors help please! Intersection of planes

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

Answer 1

x-2y-z=0
x+9y-5z=0
kx-y+z=0
it has a solution if
1{(9)(1)-(-5)(-1)}+2{(1)(1)-(-5)(k)}-1{(1)(-1)-(9)(k)}=0
1(9-5)+2(1+5k)-1(-1-9k)=0
4+2+10k+1+9k=0
19k=7
|■(1&-2&-1@1&9&-5@k&-1&1)|=0
K=7/19

Answer 2

Thank you!!!!