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Question

The vectors a,b,c and d are such that a×b=c×d and a×c=b×d. Which of the following is\are correct?
1. (ad)×(bc)=0
2. (a×d)×(b×c)=0
Select the correct answer using the code given below :

A
1 only
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B
2 only
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C
Both 1 and 2
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D
Neither 1 nor 2
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Solution

The correct option is A 1 only
Solution:
Given that:
a×b=c×d and a×c=b×d
1.(ad)×(bc)
=a×ba×cd×b+d×c
=c×db×d+b×dc×d
=0
Statement 1 is correct.
2.(a×d)×(b×c)
=[{(a×d).c}b][{(a×d).b}c]
0
Statement 2 is incorrect.
Hence, A is the correct option.

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