The points (5, -4, 2), (4, -3, 1), (7, -6, 4) | vedclass

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(D) Let the given points be $A(5, -4, 2)$,$B(4, -3, 1)$,$C(7, -6, 4)$,and $D(8, -7, 5)$.Calculate the vectors:$\vec{AB} = (4-5, -3-(-4), 1-2) = (-1, 1

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None of these

Vedclass · Answer

(D) Let the given points be $A(5, -4, 2)$,$B(4, -3, 1)$,$C(7, -6, 4)$,and $D(8, -7, 5)$.Calculate the vectors:$\vec{AB} = (4-5, -3-(-4), 1-2) = (-1, 1, -1)$$\vec{BC} = (7-4, -6-(-3), 4-1) = (3, -3, 3)$$\vec{CD} = (8-7, -7-(-6), 5-4) = (1, -1, 1)$$\vec{DA} = (5-8, -4-(-7), 2-5) = (-3, 3, -3)$Note that $\vec{BC} = -3\vec{AB}$ and $\vec{DA} = 3\vec{AB}$.Since the vectors are collinear,the points $A, B, C, D$ lie on a single straight line.Therefore,they do not form a polygon (rectangle,square,or parallelogram).Hence,option $(d)$ is correct.

The points $(5, -4, 2), (4, -3, 1), (7, -6, 4)$ and $(8, -7, 5)$ are the vertices of

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