Diketahui titik A (1,-2,-8) dan titik B (3,-4,0). Titik P terletak pada perpanjangan AB sehingga AP =-3 PB. Jika P vektor posisi titik P, maka P = ......
xkuadratz
![AP =-3 PB \\ p-a = -3(b-p) \\ p-a = 3p-3b \\ 3b-a = 3p-p \\ 3b-a=2p \\ p= \frac{3b-a}{2} \\ \\ p=3( \left[\begin{array}{ccc}3\\-4\\0\end{array}\right] - \left[\begin{array}{ccc}1\\-2\\-8\end{array}\right]) / 2 \\ \\ p= \frac{\left[\begin{array}{ccc}6\\-6\\24\end{array}\right]}{2} \\ \\ p=\left[\begin{array}{ccc}3\\-3\\12\end{array}\right]](https://tex.z-dn.net/?f=AP+%3D-3+PB+%5C%5C+p-a+%3D+-3%28b-p%29+%5C%5C+p-a+%3D+3p-3b+%5C%5C+3b-a+%3D+3p-p+%5C%5C+3b-a%3D2p+%5C%5C+p%3D+%5Cfrac%7B3b-a%7D%7B2%7D+%5C%5C+%5C%5C+p%3D3%28+%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D3%5C%5C-4%5C%5C0%5Cend%7Barray%7D%5Cright%5D+-+%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%5C%5C-2%5C%5C-8%5Cend%7Barray%7D%5Cright%5D%29+%2F+2+%5C%5C+%5C%5C+p%3D+%5Cfrac%7B%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D6%5C%5C-6%5C%5C24%5Cend%7Barray%7D%5Cright%5D%7D%7B2%7D+%5C%5C+%5C%5C+p%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D3%5C%5C-3%5C%5C12%5Cend%7Barray%7D%5Cright%5D "AP =-3 PB \\ p-a = -3(b-p) \\ p-a = 3p-3b \\ 3b-a = 3p-p \\ 3b-a=2p \\ p= \frac{3b-a}{2} \\ \\ p=3( \left[\begin{array}{ccc}3\\-4\\0\end{array}\right] - \left[\begin{array}{ccc}1\\-2\\-8\end{array}\right]) / 2 \\ \\ p= \frac{\left[\begin{array}{ccc}6\\-6\\24\end{array}\right]}{2} \\ \\ p=\left[\begin{array}{ccc}3\\-3\\12\end{array}\right]")
15 votes
Thanks 47
flatonigiri
Maaf itu ada yang salah seharusnya kan A tidak di kali dengan 3
flatonigiri
B nya saja
Saferatwin
Jadi nantinya 1 ,-3,12???
Ish24
jadinya itu 2,-5,4
en1213
4,-5,4