The fourth vertex of the parallelogram whose consecutive vertices are (2, 4, –1), (3, 6,

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The fourth vertex of the parallelogram whose consecutive vertices are (2, 4, –1), (3, 6, –1), (4, 5, 1) is

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(3, 3, 1)

(4, –2, –4)

(2, 2/3, 2)

(5, 0, 1)

answer is A.

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Detailed Solution

In a parallelogram, if $A, B, C$ are vertices in order, then the fourth vertex is $D = A + C - B$

Here $A (2, 4, - 1), B (3, 6, - 1), C (4, 5, 1)$

The fourth vertex

$\begin{array}{rcl} D & = & A + C - B \\ = & (2 + 4 - 3, 4 + 5 - 6, - 1 + 1 + 1) \\ = & (3, 3, 1) \end{array}$

Therefore, the fourth vertex is $(3, 3, 1)$

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