Question

If the three successive vertices of a parallelogram have the position vectors as, $A(-3,-2,0);B(3,-3,1)$ and $C(5,0,2).$ Then find :
position vector of the fourth vertex $D$

Answer 1

$A(-3,-2,0)B(3,-3,1)C(5,0,2)$ if $3$ vertices are given $(x_1,y{,}_1,z_1)(x_2,y_2,z_2)$ and $(x_3,y_3,z_3)$

the fourth vertex is given by,$(x_1+x_3-x_2,y_1+y_3-y_2,z_1+z_2-z_2)$

$4^{th}$ vertex $=(-3+5-3,-2+0+3,0+2-1)$

$\Rightarrow (-1,1,1)$

The vertex $D$ position vector is $(-1,1,1)$