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Question

The altitude of a parallelopiped whose three coterminous edges are the vectors,¯A=^i+^j+^k;¯B=2^i+4^j^k & ¯C=¯i+¯j+3^k with ¯A and ¯B as the sides of the base of the parallelopiped is

A
2/19
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B
4/19
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C
238/19
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D
none
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Solution

The correct option is B 238/19
A×B=(^i+^j+^k)×(2^i+4^j^k)=5^i+3^j+2^k

Area of base S=|A×B|=(5)2+32+22=38

Volume of parallelepiped, V=C.(A×B)

V=(^i+^j+3^k).(5^i+3^j+2^k)=4

Altitude h=VS=438=23819

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