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Let a = 2i + j - 2k and b = i + j. Let c be a vector such that |c - a| = 3, |(a×b)×c| = 3 and the angle between c and a×b be 30°. Then a·c is equal to:

1. 1/8
2. 25/8
3. 2
4. 5

Correct answer: 2

Solution

a=(2,1,-2), a x b=(2,-2,1) with |a x b|=3. From |(a x b) x c|=3=3|c|sin30 -> |c|=2. Then |c-a|^2=9 -> |c|^2-2(a.c)+|a|^2=9 -> 4-2(a.c)+9=9 -> a.c=2.

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