Question

Show that the points (3,-2,4),(1,1,1)and (-1,4,-2) are collinear

Answer 1

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Answer 2

Answer:

Given the points A(3,-2,4) , B(1,1,1) and C(-1,4,-2)  

we have to show that given points are collinear.

The above points are collinear if their direction ratios are proportional.

Direction ratios of AB = $(3-1,-2-1,4-1)=(2,-3,3)$

Direction ratios of BC = $(-1-1,4-1,-2-1)=(-2,3,-3)$

$a_1=2,b_1=-3,c_1=3,a_2=-2,b_2=3\:and\:c_2=-3$

$\frac{a_1}{a_2}=\frac{2}{-2}=-1$

$\frac{b_1}{b_2}=\frac{-3}{3}=-1$

$\frac{c_1}{c_2}=\frac{3}{-3}=-1$

Since, $\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}=-1$

Therefore, The points A,B and C are collinear.

Hence Proved.