Question

Please help meGiven a triangle ABC, AM = 2/3 * AB, AN = 3/2 * AC. Line MN intersects BC at point K. Find coordinates of vector AK in basis from vector AB and AC..

Answer 1

`\begin{gathered} AM=(2)/(3)AB \\ AN=(3)/(2)AC \end{gathered}`
`\begin{gathered} MN=MK+NK\to(1) \\ MN=AM+AN\to(2) \\ MN=NK+AK+AM\to(3) \\ AN=AK+NK\to(4) \end{gathered}`
`\begin{gathered} NK=AN-AK\to(4) \\ MN=(AN-AK)+AK+AM \end{gathered}`