Posted by **Baljinder** on Monday, June 10, 2013 at 5:18pm.

Without solving , determine the points of intersection of the line r= (5,-9,3) +k (1,-12,2] and the plane [x,y,z]= (4,-15,-8) + s[1,-3,1] + t[2,3,1], if any exist.

- Calculus Grade 12 -
**Reiny**, Monday, June 10, 2013 at 8:20pm
line r= (5,-9,3) +k (1,-12,2]

x = 5 + k

y = -9 - 12k

z = 3 + 2k

plane:

x = 4 + s + t

y = -15 - 3s + 3t

z = -8 + s + t

so

4 + s+ t = 5 + k

s + t - k = 1 , #1

-15 - 3s + 3t = -9 - 12k

-3s + 3t + 12k = 6 , #2

-8 + s + t = 3 + 2k

s + t - 2k = 11 , #3

#1 - #3:

k = -10

sub back into line equation:

r = (5,-9,3) - 10(1,-12,2)

= (-5 , 111 , -17)

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