Q86 / 150 · MHT CET 2018 · Mathematics

If a → , b → , c → are mutually perpendicular vectors having magnitude 1,2,3 respectively, then [ a → + b → + c → b → − a → c → ]=

  • A
    0
  • B
    6
  • Correct answer
    C
    12
  • D
    18

Solution

Given, |a→|=1, |b→|=2, |c→|=3 and 
a→.b→=0=b→.c→=c→.a→ (as the three vectors are mutually perpendicular)

So, 
[(a→+b→+c→)×(b→−a→)].c→
=[a→×b→−0+0−b→×a→+c→×b→-c→×a→].c→
=[2(a→×b→).c→+(c→×b→).c→−(c→×a→).c→]
=2(a→×b→).c→+0−0
=2[a→ b→ c→]
= 2 · 1 · 2 · 3
= 1 2

Hence, the correct answer is option: 'C'.

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