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:

The proof is explained below.

Step-by-step explanation:

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 are

$<x_2-x_1,y_2-y_1,z_2-z_1>=<1-3,1-(-2),1-4>=<-2,3,-3>$

Direction ratios of BC are

$<-1-1,4-1,-2-1>=<-2,3,-3>$

∴ $a_1=-2, b_1=3,c_1=-3$

$a_2=-2,b_2=3,c_2=-3$

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

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

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

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

The points A,B and C are collinear.