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Question

If the vectors a^i+^j+^k, ^i+b^j+^k and ^i+^j+c^k are coplanar (abc1), then the value of abc(a+b+c)=

A
2
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B
2
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C
0
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D
1
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Solution

The correct option is B 2
The vectors are coplanar.
Therefore, their scalar triple product is zero.
∣ ∣a111b111c∣ ∣=0
a(bc1)(c1)+(1b)=0
abc(a+b+c)=2

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