## Zenmo one year ago Use the dot product to determine whether the parallelogram is a rectangle. A( 3, 2, -1), B ( -2, 2, -3), C( 3, 5, -2), D( -2, 5, -4).

1. Zenmo

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2. UnkleRhaukus

$\vec{AB}\cdot\vec{AC}=\vec{AB}\cdot\vec{BD}=\vec{CD}\cdot\vec{AC}=\vec{CD}\cdot\vec{BD} =$

3. UnkleRhaukus

$=\langle-5, 0, -2\rangle\cdot\langle0, 3, -1\rangle \\=$

4. Zenmo

(-5 x 0) + (0 x 3) + (-2 x -1 ) = 0 + 0 + 2 = 2. The parallelogram is not a rectangle, since the dot product isn't 0?

5. UnkleRhaukus

yeah, the opposite sides might be parallel, but the adjacent are not perpendicular

6. Zenmo

Thanks! :)