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If vector a = (4i + 5j - k), vector b = (i - 4j + 5k) and vector c = (3i + j - k), find a vector d which is perpendicular to both vector (a and b)

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If vector a = (4i + 5j - k), vector b = (i - 4j + 5k) and vector c = (3i + j - k), find a vector d which is perpendicular to both vector (a and b) and for which vector (c.d) = 21.

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Consider vector d as the vector perpendicular to vector (a and b)

We know that

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