If A, B, C and D are (3,7,4), (5,-2,-3), (-4, | vedclass

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(B) The vectors representing the co-terminus edges are given by:$AB = (5-3)\hat{i} + (-2-7)\hat{j} + (-3-4)\hat{k} = 2\hat{i} - 9\hat{j} - 7\hat{k}$$A

Vedclass · Accepted Answer

$94$

Vedclass · Answer

(B) The vectors representing the co-terminus edges are given by:$AB = (5-3)\hat{i} + (-2-7)\hat{j} + (-3-4)\hat{k} = 2\hat{i} - 9\hat{j} - 7\hat{k}$$AC = (-4-3)\hat{i} + (5-7)\hat{j} + (6-4)\hat{k} = -7\hat{i} - 2\hat{j} + 2\hat{k}$$AD = (1-3)\hat{i} + (2-7)\hat{j} + (3-4)\hat{k} = -2\hat{i} - 5\hat{j} - 1\hat{k}$The volume of the parallelepiped is given by the scalar triple product $|[AB, AC, AD]| = |\vec{AB} \cdot (\vec{AC} 	imes \vec{AD})|$.This is equal to the absolute value of the determinant:$|\begin{vmatrix} 2 & -9 & -7 \ -7 & -2 & 2 \ -2 & -5 & -1 \end{vmatrix}|$$= |2(2 - (-10)) - (-9)(7 - (-4)) + (-7)(35 - 4)|$$= |2(12) + 9(11) - 7(31)|$$= |24 + 99 - 217|$$= |123 - 217| = |-94| = 94$ cubic units.

If $A, B, C$ and $D$ are $(3,7,4), (5,-2,-3), (-4,5,6)$ and $(1,2,3)$ respectively,then the volume of the parallelepiped with $AB, AC$ and $AD$ as the co-terminus edges is .... cubic units.

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