diket: koordinat A (1,p,5), B (2,-4,4) dan C (-1,2,q). jika A,B, C segaris maka nilai p+q adalah....

p =  -5 q = -2 maka p+q = (-5) +(-2) = -7

[tex] \frac{}{AB} = \left[\begin{array}{ccc}1-2\\p-(-4)\\5-4\end{array}\right] = \left[\begin{array}{ccc}-1\\p+4\\1\end{array}\right] [/tex]

[tex] \frac{}{BC} = \left[\begin{array}{ccc}2-(-1)\\-4-2\\4-q\end{array}\right] = \left[\begin{array}{ccc}3\\-6\\4-q\end{array}\right] [/tex]

Sehingga :
Karena segaris maka :
AB segaris BC atau sama saja dengan AB = BC

[tex]\left[\begin{array}{ccc}-1\\p+4\\1\end{array}\right]= k \left[\begin{array}{ccc}3\\-6\\4-q\end{array}\right][/tex]

Maka :
- 1 = k3
k = -1/3

Untuk nilai p :
p + 4 = -6k
p + 4 = -6(-1/3)
p + 4 = 2
p = 2 - 4
p = - 2

Untuk nilai q :
1 = k (4 - q)
1 = (-1/3) ( 4 - q)
- 3 = 4 - q
- 3 - 4 = - q
- 7 = - q
q = 7
 
Maka untuk p + q
= - 2 + 7
= 5