If the three consecutive vertices of a parall | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) Let the vertices of the parallelogram be $A(1, 2, 3)$,$B(-1, -2, -1)$,$C(2, 3, 2)$,and $D(x, y, z)$.In a parallelogram,the diagonals bisect each o

Vedclass · Accepted Answer

$(4, 7, 6)$

Vedclass · Answer

(B) Let the vertices of the parallelogram be $A(1, 2, 3)$,$B(-1, -2, -1)$,$C(2, 3, 2)$,and $D(x, y, z)$.In a parallelogram,the diagonals bisect each other. This means the midpoint of diagonal $AC$ is the same as the midpoint of diagonal $BD$.Midpoint of $AC = (\frac{1+2}{2}, \frac{2+3}{2}, \frac{3+2}{2}) = (\frac{3}{2}, \frac{5}{2}, \frac{5}{2})$.Midpoint of $BD = (\frac{-1+x}{2}, \frac{-2+y}{2}, \frac{-1+z}{2})$.Equating the midpoints:$\frac{-1+x}{2} = \frac{3}{2} \implies -1+x = 3 \implies x = 4$.$\frac{-2+y}{2} = \frac{5}{2} \implies -2+y = 5 \implies y = 7$.$\frac{-1+z}{2} = \frac{5}{2} \implies -1+z = 5 \implies z = 6$.Thus,the fourth vertex $D$ is $(4, 7, 6)$.

If the three consecutive vertices of a parallelogram are $A(1, 2, 3)$,$B(-1, -2, -1)$,and $C(2, 3, 2)$,then its fourth vertex is:

Similar Questions

If $A(0,1,2)$,$B(2,-1,3)$,and $C(1,-3,1)$ are the vertices of a triangle,then the distance between its circumcentre and orthocentre is

Let $ABCD$ be a tetrahedron in which the coordinates of each of its vertices are in arithmetic progression with the same common difference. If the centroid $G$ of the tetrahedron is $(2, 3, k)$,then the distance of $G$ from the origin is

The incentre of the triangle whose vertices are $P(0,3,0)$,$Q(0,0,4)$,and $R(0,3,4)$ is

Let $A(1, 2, 3)$, $B(-1, 4, 6)$, $C(0, -6, 4)$, and $D(1, 1, 1)$ be the vertices of a tetrahedron. Let $G$ be its centroid and $G_1$ be the centroid of its face $BCD$. Then $\frac{AG_1}{AG} =$

The angle between two diagonals of a cube is

Vedclass Test Series

Exam Paper Generator

Online Exam Module