Question
The ordered pair $$\left( {\lambda ,\,\mu } \right)$$ such that the points $$\left( {\lambda ,\,\mu ,\, - 6} \right),\,\left( {3,\,2,\, - 4} \right)$$ and $$\left( {9,\,8,\, - 10} \right)$$ become collinear is :
A.
$$\left( {3,\,4} \right)$$
B.
$$\left( {5,\,4} \right)$$
C.
$$\left( {4,\,5} \right)$$
D.
$$\left( {4,\,3} \right)$$
Answer :
$$\left( {5,\,4} \right)$$
Solution :
If the given points $$\left( {\lambda ,\,\mu ,\, - 6} \right),\,\left( {3,\,2,\, - 4} \right)$$ and $$\left( {9,\,8,\, - 10} \right)$$ are collinear then
$$\eqalign{
& \frac{{\lambda - 3}}{{9 - 3}} = \frac{{\mu - 2}}{{8 - 2}} = \frac{{ - 6 + 4}}{{ - 10 + 4}} \cr
& \Rightarrow \lambda = 5,\,\mu = 4 \cr} $$