How to show two lines intersect in a vector question.

Can you explain why you need the values for a and b to find the point of intersection?In summary, the two given equations represent two straight lines with scalar parameters a and b. To find their point of intersection, the values of a and b need to be determined, which is the task at hand.
  • #1
hanosh
2
0
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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  • #2
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?
 
  • #3
no they have not given me the value of a or b
 
  • #4
Well, no, of course not. That's your job to find them.
 

1. How can I tell if two lines intersect in a vector question?

To determine if two lines intersect in a vector question, you can use the vector equation of each line and set them equal to each other. If the resulting system of equations has a unique solution, then the lines intersect at a single point, indicating an intersection. If the system has no solution, the lines are parallel and do not intersect. If the system has infinitely many solutions, the lines overlap and intersect at all points along that line.

2. Can I use the slope-intercept form to show intersecting lines in a vector question?

Yes, you can use the slope-intercept form (y = mx + b) to show intersecting lines in a vector question. Simply set the equations of the two lines equal to each other and solve for the point of intersection. However, this method may not always be the most efficient and accurate way to show intersecting lines in a vector question.

3. Is there a specific method for showing intersecting lines in a vector question?

Yes, there are multiple methods for showing intersecting lines in a vector question. Some common methods include using the vector equation, parametric equations, or the Cartesian form. It is important to choose the method that best fits the given information and equations in the vector question.

4. How do I know if two vectors are parallel or perpendicular?

If the dot product of two vectors is equal to zero, then the vectors are perpendicular. If the dot product is equal to a non-zero value, then the vectors are parallel. You can also determine if two vectors are parallel by comparing their slopes or by using the cross product.

5. Can two lines intersect in more than one point in a vector question?

No, two lines can only intersect at one point in a vector question. This is because, in a two-dimensional plane, two lines can only have one point in common. If two lines appear to intersect at multiple points, they are either the same line or are skew lines that do not actually intersect.

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