If A (-4,5, P ), B (3,1,4) and C (-2,0, q ) are the vertices of a triangle A B C and G(r, q, 1) is its centroid, then the value of 2 p+q-r is equal to

Step-by-step solution

A (-4,5, p ), B (3,1,4) and C (-2,0, q ) are vertices of triangle A B C Centroid ( x₁+x₂+x₃ 3 , y₁+y₂+y₃ 3 , z ₁+ z ₂+ z ₃ 3 ) ( r , q , 1) ( -4+3-2 3 , 5+1+0 3 , p +4+ q 3 ) aligned & r =-1, q =2, p + q +4=3 & r =-1, q =2, p =-3 & 2 p + q - r =2(-3)+2+1 & =-6+2+1 & =-3 aligned