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Question

The number of vectors of unit length perpendicular to the vectors a=2i^+j^+2k^ and b=j^+k^ is
(a) one
(b) two
(c) three
(d) infinite

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Solution

Unit vector perpendicular to a and b is ±a×ba×b for a=2i^+j^+2k^ and b=j^+k^a×b=i^j^k^212011a×b=i^1-2 -j^2-0+k^2-0

a×b=-12+22+22=9=3
unit vector perpendicular to both a and b is ±-i^-2j^+2k^3=±-i^3-2j^3+2k^3

i.e. number of vectors of unit length perpendicular to the vectors a and b is two.

Hence, the correct answer is option B.

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