Calculus Grade 12
posted by Baljinder .
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.

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)