Question

Vector Calculus Problem: I have to find where these two planes intersect. I know this should be really easy for me but for some reason i'm not getting it

3x-2y+z=10 and -4x+5y+2z=14

Answer 1

lets see where they hit the xy plane when z=0

3x-2y=10
-4x+5y=14

y = 82/7
x = 78/7


lets see where they cross when z=....10

Answer 2

3x-2y+10=10

3x -2y = 0
-4x+5y=-6

y= -18/7
x = -12/7

Answer 3

so we have 2 points now of intersection I believe; lets line them up :)

Answer 4

( 78/7, 82/7, 0)
-(-12/7,-18/7,10)
-----------------
< 90/7,100/7,-10>

Answer 5

t< 9,10,-1/7>

x=78x+9t
y=82y+10t
z=-(1/7)t

maybe?

Answer 6

the wolf might suggest its t<9,10,-7>

Answer 7

<9/15, 10/15,-7/15>

<9,10,-7> = vector parallel to line