Punch said:The equation of the lines l1 and l2 are are r=(4+t)i + (a+3t)j + (2-3t)k and r=(1-2s)i + (1-s)j + (1+s)k respectively, where t and s are real parameters. It is given that the lines intersect. Find the value of a.
When two lines intersect, it means that they cross or meet at a single point. This point is known as the intersection point and is the solution to the equations of the two lines.
Lines intersect if they have different slopes. If two lines have the same slope, they are parallel and will never intersect. Additionally, if the lines have the same y-intercept, they will also never intersect.
The value of a represents the x-coordinate of the intersection point. It is important because it gives us the exact location where the two lines intersect and allows us to solve for the y-coordinate as well.
The value of a can be found by setting the equations of the two lines equal to each other and solving for x. This will give us the x-coordinate of the intersection point, which is the value of a.
No, two lines can only intersect at one point. If they intersect at more than one point, then they are not considered distinct lines and are actually the same line.