Question

show that the points A(-2,3,5)B(1,2,3)C(7,0,1)are collinear

Answer 1

Find the distances AB, BC and AC using the following formula
$s \: = \sqrt{ {(x1 - x2)}^{2} + {(y1 - y2)}^{2} + {(z1 - z2)}^{2} }$
And you will find that sum of two of the distances will be equal to third one.
That will prove that the points lie on the same line.
Hope this helps

Answer 2

Hey !!

We know that points are said to be collinear if they lie on the line.

We know the Distance formula

√(x₂ - x₁)² + (y₂ - y₁)² + (z₂ - z₁)²

AB = √( 1  + 2 )² = ( 2 - 3 ) ² + ( 3 - 5 )²

         = √ 9 + 1 + 4

         = √14

BC = √(7 - 1)² + (0 - 2)² + (-1 -3 )²

      = √36 + 4 + 16

      = 2√14

CA = √( 7 + 2)² + (0 - 3)² + (-1-5)²

     = √81 + 9 + 36

     = √126

     = 3√14

Thus, AB + BC = CA. Hence A,B and C are collinear.

GOOD LUCK !!