Question

Consider the planes 1x+5y+5z=1 and 1x+5z=0
A) Find the unique point P on the y-axis which is on both planes.
B) Find the unit vector u with positive first coordinate that is parallel to both planes.
C) Use parts (A) and (B) to find a vector equation for the line of intersection of the two planes, r(t) =

Answer 1

part A is (0,1/5,0)

Answer 2

A) Yes, the intersection point is on y = 1/5
-> < 0, 1/5, 0>
B) The vector parallel to both planes is the cross product vector of normal vectors:
< 1, 5, 5 > X < 1, 0, 5 >

Answer 3

C) just combine the corresponding coordinate of A and B

Can you do it?

Answer 4

thank you

Answer 5

wait i got only the y coordinate of part C right?

Answer 6

Did you find B?

Answer 7

* part B?

Answer 8

yes i got <25/sqrt(650),0,-5/sqrt(650)>
that part was correct

Answer 9

= 1/ √ 650 < 25, 0, -5 >
=> Line of intersection of 2 planes
= < 25* t /√ 650 , 1/5, -5 t/ √ 650 >

Answer 10

thank you i was forgetting the t's

Answer 11

r(t) = sum of the component of i + j + k