Question

the circumcenter of the triangle formed by the point (1,2,3),(3,-1,5),(4,0,-3)​

Answer 1

Answer:

We have

A (1,2,3)

B (3,−1,5)

C (4,0,−3)

Direction ratio of AB=(3−1,−1−2,5−3)=(2,−3,2)

Direction ratio of AC=(4−1,0−2,−3−3)=(3,−2,−6)

Now let us find dot product

AB⋅AC=(2,−3,2)(3,−2,−6)

=6+6−12=0

As dot product of AB and AC is 0, hence

Triangle is right angled at A.

For right angled triangle, circumcentre is mid point of hypotenuse.

Hence Circumcentre = Mid point if BC

=(23+4,2−1+0,25−3)

=(27,−21,1)