Posted by **j** on Saturday, May 26, 2012 at 8:12am.

7. Where does the line r = (1, 2, -5) + t (2, -3, 1) meet the plane 2x + 5y - 3z = 6?

- Calculus -
**Reiny**, Saturday, May 26, 2012 at 8:37am
the line can be written as

x = 1 + 2t

y = 2 - 3t

z = -5 + t

sub that into your plane equation and see if it satisfies the equation

- Calculus -
**Reiny**, Saturday, May 26, 2012 at 8:42am
slightly mis-read the question.

continue from above

2(1+2t) + 5(2-3t) - 3(-5+t) = 6

2 + 4t + 10 - 15t + 15 - 3t = 6

-14t = -21

t = -21/-14 = 3/2

x = 1 + 2(3/2) = 4

y = 2 - 3(3/2) = -5/2

z = -5 + 3/2 = -7/2

the line intersects at (4, -5/2, -7/2)

- Calculus -
**j**, Saturday, May 26, 2012 at 8:53am
thanks reiny!

- Calculus -
**Reiny**, Saturday, May 26, 2012 at 8:59am
welcome

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