Question

A(3,1,5), B(1,1,9) and C(0,5,1) are the vertices of a triangle then find the position vector of the centroid of you.​

Answer 1

Answer:

Let the third vertex be C=x

i

+y

j

+z

k

and A=(1,1,0), B=(2,−1,1), G=(0,0,1)

Hence G=(

3

x

1

+x

2

+x

3

,

3

y

1

+y

2

+y

3

,

3

z

1

+z

2

+z

3

)

(0,0,1)=(

3

1+2+x

,

3

1−1+y

,

3

0+1+z

)

(0,0,1)=(

3

x+3

,

3

y

,

3

z+1

)

Hence x+3=0 gives x=−3

3

y

=0 gives y=0

And

3

z+1

=1 gives z=2

Hence C=−3

i

+2

k.

Hope it helps you