Question

Pojnts (-2,4,7). (3.-6.-8) and (1, -2,-2) are
collinear
(2) vertices of an equilateral triang
(3) vertices of isosceles triangle
(4) none of these​

Answer 1

The "option (4) none of these" is required answer.

Step-by-step explanation:

Let  A(- 2, 4, 7), B(3, - 6, - 8) and C(1, - 2, - 2) are the three points.

$AB^{2} = (3 + 2)^{2}$ + (- 6  - 4)^{2}[/tex]  + (- 8 - 7)^{2}[/tex]

= $5^{2}$ +$(- 10)^{2}$  + $(- 15 )^{2}$

= 25 + 100 + 225 =350

$BC^{2} = (1 - 3)^{2}$ +$(- 2 + 6)^{2}$  +$(- 2 + 8)^{2}$

= $( - 2)^{2}$ +$(4)^{2}$  +$(6)^{2}$

= 4 + 16 + 36 = 56

$CA^{2}$= $(1 + 2)^{2}$ +$(- 2 - 4)^{2}$  + $(- 2 - 7)^{2}$

=$(3)^{2}$ +$(- 6)^{2}$  +$(- 9)^{2}$

= 9 + 36 + 81 = 126

Check options:

(1) Collinear,  $AB^{2}$ + $BC^{2}$ = $CA^{2}$

⇒ 350 + 56 ≠ 126, it is not collinear.

(2) An equilateral triangle, All sides are are equal.

It is not isosceles triangle.

(3) An isosceles triangle, At least two sides are equal.

It is not isosceles triangle.

Hence, "option (4) none of these" is required answer.