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Question

If a=2^i3^j+5^k,b=3^i4^j+5^k and c=5^i3^j2^k, then the volume of the parallelopiped with conterminous edges a+b,b+c,c+a is

A
20
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B
10
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C
16
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D
0
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Solution

The correct option is B 16
¯¯¯a+¯¯b=5^i7^j+10^k
¯¯b+¯¯c=8^i7^j+3^k
¯¯c+¯¯¯a=7^i6^j+3^k
Volume of parallelopipe = [¯¯¯a+¯¯b¯¯b+¯¯c¯¯c+¯¯¯a]
∣ ∣5710873763∣ ∣
5[(21+18)]+7(2421)+10(48+49)
15+21+10
16 cubic units

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