Question

(1, -3,1), (2, - 1, 3), (0, 1, 2) are vertices of a triangle then its orthocentre and circumcentre are situated
at a distance of
>plz answer it guys I am not able to get this .​

Answer 1

Given:

We have been given  vertices of a triangle which are(1, -3,1), (2, - 1, 3), (0, 1, 2)

To find:

The distance of orthocentre and circumcentre.

Solution:

A = i - 3j + 1k

B = 2i - j +3k

C = 1j +2k

G = A+B+C/3

= i - j +2k

AB = B - A = i+2j+2k

BC = C - B = -2i +2j -k

CA = A - C = i-4j-k

AB.BC = -2+4-2=0[Since thedot product is 0,It is orthogonal at B]

H = B = 2i-j+3k

G = i-j+2k

|HG|= G - H = -i-k = $\sqrt{2}$  [orthocenter]

|HG| =2/3HO

|HO|= 3 $\sqrt{2}$ /2 [Circumcenter]