Exercise 1 2nd part how to prove it

# Doubt from straight lines

For vth part i did by determinant method to avoid mistakes but got wrong result

Tell where i am wrongBro in third last step there is 51k not 5k

I know but answers are not matching answer is k=31/9 and k=7 but i am getting k=17/3 and k=-4 which is incorrect

The formula of area of triangle is 1 by2 times[ ] and that you wrote in your copy is condition for collinear of three points

Thank you