Doubt from straight lines

Exercise 1 2nd part how to prove it

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

Tell where i am wrong

Bro 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


You have missed out 1/2

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Thank you