Question

jawablah soal tersebut. ​

Answer 1

[tex]AB = B-A\\AB=\left[\begin{array}{c}4\\6\\-8\end{array}\right]-\left[\begin{array}{c}10\\2\\-6\end{array}\right] \\AB=\left[\begin{array}{c}-6\\4\\-2\end{array}\right][/tex]

[tex]BP=P-B\\BP=\left[\begin{array}{c}x\\y\\z\end{array}\right]-\left[\begin{array}{c}4\\6\\-8\end{array}\right] \\BP=\left[\begin{array}{c}x-4\\y-6\\z+8\end{array}\right][/tex]

[tex]\frac{AB}{BP}=\frac{6}{4}\\\\\frac{\left[\begin{array}{c}-6\\4\\-2\end{array}\right]}{\left[\begin{array}{c}x-4\\y-6\\z+8\end{array}\right]}=\frac{6}{4}\\4{\left[\begin{array}{c}-6\\4\\-2\end{array}\right]=6\left[\begin{array}{c}x-4\\y-6\\z+8\end{array}\right]\\\\{\left[\begin{array}{c}-24\\16\\-8\end{array}\right]={\left[\begin{array}{c}6x-24\\6y-36\\6z+48\end{array}\right][/tex]

-24 = 6x - 24

0 = 6x

0 = x

16 = 6y - 36

52 = 6y

52/6 = y

26/3 = y

-8 = 6z + 48

-56 = 6z

-56/6 = z

-28/3 = z

jadi, koordinat P adalah

[tex]P={\left[\begin{array}{c}0\\\frac{26}{3} \\\frac{-28}{3} \end{array}\right][/tex]