Find the equation of the line by using vectors

[TheMathNoob]

Homework Statement

I have to find the equation of the line by using any vector a and b in a way that the line fits the triangle generated by vector addition. If you don't understand my statement, look at my attached file. You will understand what I mean by triangle. Is my solution right?

Homework Equations

The Attempt at a Solution

 

[Qwertywerty]

Essentially, it is correct.

However - There is no requirement for such constraint for t. Remember, you are writing an equation for a line; an infinite number of points are possible.
Further, you could just write the second term on the right, as t(a^→+b^→), and t can take an infinite number of values, corresponding to an infinite number of points on the line.

 

[TheMathNoob]

Essentially, it is correct.

However - There is no requirement for such constraint for t. Remember, you are writing an equation for a line; an infinite number of points are possible.
Further, you could just write the second term on the right, as t(a^→+b^→), and t can take an infinite number of values, corresponding to an infinite number of points on the line.

thanks I wasn't actually clear on the fact that the boundaries are necessary to fit the idea of triangle.