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Given vectors a=î+ĵ and b=2ĵ-k̂, a vector r satisfies r×a=b×a and r×b=a×b. Find (r)/(|r|).

1. (î+3ĵ-k̂)/(√(11))
2. (î-3ĵ+k̂)/(√(11))
3. (î+3ĵ+k̂)/(√(11))
4. (î-3ĵ-k̂)/(√(11))

Correct answer: (î+3ĵ-k̂)/(√(11))

Solution

r x a = b x a => (r-b) x a = 0 => r = b + s a; r x b = a x b => r = a + t b. Consistency gives r = a + b = (1,3,-1). So r/|r| = (i+3j-k)/sqrt(11).

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