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Q.

 Column–I Column–II
AVolume of parallelepiped determined by vectors a¯,b¯ and c¯ is 2. Then the volume of the parallelepiped determined by vectors 2(a¯×b¯),3(b¯×c¯) and (c¯×a¯) isP100
BVolume of parallelepiped determined by vectors a¯,b¯ and c¯  is 5. Then the volume of the parallelepiped determined by vectors 3(a¯+b¯),(b¯+c¯) and 2(c¯+a¯) isQ30
CArea of a triangle with adjacent sides determined by vectors a¯ and b¯ is 20. Then the area of the triangle with adjacent sides determined vectors (2a¯+3b¯) and (a¯b¯) isR24
DArea of a triangle with adjacent sides determined by vectors a¯ and b¯ is 15. Then the area of the parallelogram with adjacent sides determined vectors (a¯+b¯) and a¯ isS60

 

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a

AR, BS, CP, DQ

b

AP, BS, CR, DQ

c

AQ, BR, CP, DS

d

AS, BQ, CR, DP

answer is C.

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Detailed Solution

P[a¯   b¯   c¯]=2

[2a¯×b¯     3b¯×c¯     c¯×a¯]=6[a¯     b¯     c¯]2=6×4=24

Q[a¯     b¯     c¯]=5

6[a¯×b¯     b¯×c¯     c¯×a¯]=12[a¯     b¯     c¯]=60

R12|a¯×b¯|=20

12|(2a¯+3b¯)×(a¯b¯)|

12|2(a¯+b¯)3(a¯×b¯)|

52×40=100

S|a¯×b¯|=30|(a¯+b¯)×a¯|=|b¯×a¯|=30

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