Question

Вершины четырехугольника А(-4;-3;-2),В(2;-2;-3),С(-8;-5;1),D(4;-3;-1) докозать,что его диогональ взаимно перпендикулярно

Answer 1

А=(-4 -3-2)=3+В=(1,2)С=4D=1

Answer 2

Given Information:

The vertices of the quadrilateral are: - A(-4, -3, -2) - B(2, -2, -3) - C(-8, -5, 1) - D(4, -3, -1)

We need to prove that the diagonal of the quadrilateral is mutually perpendicular.

Solution:

To prove that the diagonal is mutually perpendicular, we need to show that the dot product of the two diagonals is zero.

Let's calculate the two diagonals of the quadrilateral:

Diagonal AC: AC = C - A = (-8, -5, 1) - (-4, -3, -2) = (-8 + 4, -5 + 3, 1 - (-2)) = (-4, -2, 3)

Diagonal BD: BD = D - B = (4, -3, -1) - (2, -2, -3) = (4 - 2, -3 - (-2), -1 - (-3)) = (2, -1, 2)

Now, let's calculate the dot product of AC and BD:

AC · BD = (-4, -2, 3) · (2, -1, 2) = (-4 * 2) + (-2 * -1) + (3 * 2) = -8 + 2 + 6 = 0

Since the dot product of AC and BD is zero, we can conclude that the diagonal of the quadrilateral is mutually perpendicular.

Therefore, the diagonal of the quadrilateral is mutually perpendicular.