Advanced Search

Question: Equation of a line (3)

Question:Equation of a line (3)

toandhsp 300 Maple
line
January 25 2012
0

Problem. Write the equation of the line Delta which parallel to the planes 

(P): 3x +12y -3z -5 = 0, (Q): 3x -4y +9z + 7 = 0

and cuts two the lines

(d1): x = 2t -5, y = -4t + 3, z = 3t -1

(d2): x = -2m + 3,  y = 3m  - 1, z = 4m + 2.

This is my idea.

1) Put A(2t -5, -4t + 3, 3t -1) and B(-2m + 3, 3m  - 1, 4m + 2).

2) Find coordinates of vector AB.

3) Because Delta parallel to the planes (P) and (Q), therefore Delta parallel to line of intersection of (P) and (Q). Let v be direction vector of this line. We have AB and v are collinear. 

Please help me. Thank you very much.
Please Wait...