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Question

Find a vector perpendicular to each of the vectors a+b and ab, where a=i+j+k,b=i+2j+3k.

A
i2j+2k
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B
0
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C
i3j+2k
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D
None of these
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Solution

The correct option is D None of these
a+b=2^i+3^j+4^kab=0^i^j2^k(a+b)×(ab)=∣ ∣ ∣^i^j^k234012∣ ∣ ∣=i(6+4)^j(4)+^k(2)=2^i+4^j2^k=2(^i+2^j^k)
Therefore a vector perpendicular to each of the vectors a+b and ab is ^i+2^j^k

Hence the option D (None of these) is the correct answer.

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