Homework Help: Calculus

Posted by Melissa on Saturday, April 7, 2012 at 1:53pm.

Explain fully please and thank you! =)

Determine the point of intersection of the lines L1: r= (1,3,7) + s(1,2,-2),seR and L2: v=(0,2,-3) +t(1,1,4), teR.

a) P(1,3,1)
b P(1,3,7)
c) The lines coincide
d) no point of intersection

Calculus - Reiny, Saturday, April 7, 2012 at 2:55pm
if they intersect:
s+1 = t+0 ----> t = s+1
and
2s+3 = t+2 ----> t = 2s+1
and
-2s+7 = 4t-3

using the first two equations
2s+1 = s+1
s = 0 , then t=1

test in 3rd equation ...
LS = -2s+7 = 0 + 7 = 7
RS = 4t-3 = 4-3 = 1 ≠ LS

so they cannot intersect
Do they coincide?
If they did, they should have the same direction vectors ...
the first has direction (1,2,-2) and the second has direction ( 1,1,4) , so they are not parallel

conclusion: We are looking at two lines which are not parallel and which do not intersect

Answer this Question

Related Questions

Math(Calculus) - Ok I have a bunch of questions, please bare with me and i'd...
Math-Linear Systems - Determine the point of intersection. (a) y = 4x + 6 y = -x...
Vectors - I am really lost and confused! Consider the lines r = (1,-1,1) + t(3,2...
Calculus - 10. Consider the lines [x,y,z] = [4,7,-1] + t[4,8,-4] and [x,y,z] = [...
Math - 1. Imagine driving down a mountainside. You see a sign indicating there ...
Geometry - Letting L1=ax+by+c=0 and L2=px+qy+r=0. The equation of anyline ...
calculus - Determine the coordinates of the point of intersection of the two ...
Anonymous - Give the exact intersection point for the equations f(x)=4sin^2x+...
CALCULUS - FOR EACH PAIR OF LINES, DETERMINE SIZE OF ACUTE ANGLE, TO THE NEAREST...
calculus - the graphs of f(x0=x^3 and g(x)=3x+5 have one intersection point. ...

For Further Reading

First Name:
School Subject:
Answer: