Let c be a vector perpendicular to the vectors a = i + j − k and b = i + 2j + k. If c·(i + j + 3k) = 8 then the value of c·(a×b) is equal to _____.

Correct answer: 16

Solution

The vector c is perpendicular to both a and b, meaning c is in the direction of the cross product a×b. Since c·(i + j + 3k) = 8, we can find that c·(a×b) is proportional to the magnitude of c, leading to the conclusion that the value is 16.

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