Posted by Alex on Monday, April 7, 2008 at 9:49pm.
I am really lost and confused!
Consider the lines r = (1,-1,1) + t(3,2,1) and r = (-2,-3,0) + u(1,2,3).
a) Find their point of intersection.
b) Find a vector equation for the line perpendicular to both of the given lines that passes through their point of intersection.
For a I got the equations
3t-1u+3 = 0
2t-2u+2 = 0
t-3u+1 = 0
Then I put 2 and 3 together and got u = -4.
In the back of the book the answers says (-2, -3, 0). So am I already wrong?
2) Show that the lines r = (4,7,-1) + t(4,8,-4) and r = (1,5,4) + u(-1,2,3) intersect at right angles and find the point of intersection.
Can someone please walk me through these?
- Vectors - Reiny, Monday, April 7, 2008 at 10:11pm
When I solved equations 2 and 3 I got u=0 and t=-1, giving me r = (-2,-3,0) in both r = ... equations.
check your arithmetic
for the second, if they are perpendicular, then the dot product of their directions vectors should be zero
(4,8,-4)∙(-1,2,3) = -4 + 16 - 12 = 0
so they are perpendicular.
For the intersection point do exactly the same thing you did for the first one without making arithmetic errors.
BTW, your equations for the first one were correct.
Answer This Question
More Related Questions
- Calculus - Consider the planes given by the equations 2y−2x−z=2 x...
- Math - Equations of plane(check) - Consider the plane that contains points A(2,...
- Math - Equations of plane(check) - Consider the plane that contains points A(2,3...
- math - A vector equation for a given straight line is r = (i + 3j) + lambda (-i...
- vectors - 3 planes; $: x+2y-2z-6=0 %: 2x-y+z+8=0 £: 2x-y+2z+3=0 (a)(i)Find the ...
- Vectors - 3 planes; $: x+2y-2z-6=0 %: 2x-y+z+8=0 £: 2x-y+2z+3=0 (a)(i)Find the ...
- Discrete Math: Equations of Line in a Plane - I'm stuck on these questions. Can ...
- Math: Equations of Line in a Plane - I'm stuck on these questions. Can you ...
- math2 - I was solving a problem. In It r have been given that two lines are ...
- Math: Vectors - Find any vector w that is perpendicular to both vector "u = 3j...