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Q.

Let OA, OB, OC be the co-terminal edges of a rectangular parallelopiped of volume V and let P be the vertex opposite to O. Then $[\vec{AP} \vec{BP} \vec{CP}] =$

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a

2V

b

12V

c

0

d

$3 \sqrt{3} V$

answer is A.

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$OP = a + b + c AP = b + c BP = c + a CP = a + b [a b c] = ν [AP BP CP] = 2 [a b c] = 2 ν$

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Let OA, OB, OC be the co-terminal edges of a rectangular parallelopiped of volume V and let P be the vertex opposite to O. Then AP→ BP→ CP→=