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)
Answer This Question
Related Questions
 Calculus  Consider the line through the points (3,2,5) and (1,1,1). Consider ...
 math  L is a straight line in xy plane. its equation is in the form y8=m(x1...
 Math  Determine whether the following statements are always,sometime, or never ...
 calculus  Two commercial airplanes are flying at an altitude of 40,000 ft ...
 Calculus Grade 12  Find the equation of the plane that passes through the point...
 Physics  A Boeing 747 "Jumbo Jet" has a length of 55.9 m. The runway on which ...
 maths  geometry  In a space with an orthonormal coordinate system consider the...
 12th grade calculus  Let f(x)=[x^39x] []  absolute value a. does f'(x) ...
 Calculus  a) Find parametric equations for the line through (4, 1, 4) that is ...
 Geometry  4.Determine which point does not lie on the graph of the line y=x3 a...
More Related Questions