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Question

The value of a-bb-cc-a is ?


A

0

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B

1

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C

2

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D

None of the above.

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Solution

The correct option is A

0


Explanation for the correct option:

We can write a-bb-cc-a as a-b.b-c×c-a

Now to solve it we will do the cross product of two vectors b-c and c-a.

=a-b·(b×c-b×a-c×c+c×a)=a-b·(b×c-b×a+c×a)[c×c=0]=a-b·(b×c+a×b+c×a)

Now we will be finding the dot product of all the terms inside the bracket with a-b.

=a·b×c+a·a×c+a·c×a-b·b×c-b·a×b+b·c×a

Now we know that a×c is perpendicular to a,b×c is perpendicular to band a×b is perpendicular to b and taking dot products of the perpendicular vectors gives 0.

a·b×c-b·c×a

We can rewrite it as

a·b×c-a·b×c=0

Therefore, a-bb-cc-a is equal to 0.

Hence, the correct answer is option (A).


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