Question

find the position vector of centroid of a triangle vertices having position vector a^,b^,c^​

Answer 1

Answer:

Step-by-step explanation:

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

.