How to show two lines intersect in a vector question.

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To determine if the two lines intersect, the equations must be analyzed to find values for the scalar parameters a and b that yield the same position vector R. The lines are defined by R= 17i -9j+9k +a (3i+j+5k) and R=15i - 8j - k + b (4i + 3j). The goal is to show that there exist values for a and b such that both equations produce the same vector, indicating an intersection point. The discussion emphasizes the necessity of solving for a and b to find the position vector of the intersection. Ultimately, the lines can intersect if appropriate values for a and b are identified.
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This is a question I am stuck on and id really like some help pleasezzz !


Two straight lines are given by the equations:

R= 17i -9j+9k +a (3i+j+5k)
R=15i - 8j - k + b (4i + 3j )

where a and b are scalar parameters.Show that these lines intersect and find the postion vector of their point of intersection.


The attempt at a solution
 
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hanosh said:
This is a question I am stuck on and id really like some help pleasezzz !


Two straight lines are given by the equations:

R= 17i -9j+9k +a (3i+j+5k)
R=15i - 8j - k + b (4i + 3j )

where a and b are scalar parameters.Show that these lines intersect and find the postion vector of their point of intersection.


The attempt at a solution
What have you tried? Are there values for a and b where your two equations for R give the same value?
 
no they have not given me the value of a or b
 
Well, no, of course not. That's your job to find them.
 

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