Vectors

[LikeA'13OSS]

Whats is the line equation of a line in terms of ax+by=c When the vector equation is:

r=(1i+2j)+t(-2i+3j) where t is a scalar

And if you could tell me the method as well please do

thanks

[dessskris]

do you realise that:

x=1-2t

and

y=2+3t

?

from there, you express t in terms of each x and y, and combine both equations to get the desired cartesian equation.

feel free to ask further if unclear.

[aldld]

Alternatively you could note that the vector that is being multiplied by t (-2i+3j) determines the direction of the line. So you can find the slope of the line to be -3/2.

You can also tell from the equation that the line passes through the point (1, 2) (from the 1i+2j term) and using that, along with the slope, you can find the equation of the line.

Feel free to ask if you'd like any clarification.