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Find the vector vec(p) which is perpendi...

Find the vector `vec(p)` which is perpendicular to both `vec(alpha) = 4hat(i) + 5hat(j) - hat(k)` and `vec(beta) = hat(i) - 4hat(j) + 5hat(k)` and `vec(p).vec(q) = 21`, where `vec(q) = 3hat(i) + hat(j) - hat(k)`.

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