Question

Verify that the points (3,-2,4),(1,0,-2) and (-1,2,-8) are collinear.​

Answer 1

Step-by-step explanation:

Three points A,B,C are collinear if direction ratios of AB and BC are proportional.

A(2,3,4) and B(−1,−2,1)

Direction ratios =−1−2,−2−3,1−4

=−3,−5,−3

So, a

1

=−3,b

1

=−5,c

1

=−3

B(−1,−2,1) and C(5,8,7)

Direction ratios =5−(−1),8−(−2),7−1

=6,10,6

so, a

2

=6,b

2

=10,c

2

=6

Now,

a

1

a

2

=

−3

6

=−2

b

1

b

2

=

−5

10

=−2

c

1

c

2

=

−3

6

=−2

Since

a

1

a

2

=

b

1

b

2

=

c

1

c

2

=−2

Therefore, A,B,C are collinear.