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Let vec(a) = hat(i) + hat(j) + hat(k), v...

Let `vec(a) = hat(i) + hat(j) + hat(k), vec(b) = 4hat(i) - 2hat(j) + 3hat(k)` and `vec(c) = hat(i) - 2hat(j) + hat(k)` and find a vector of magnitude 6 units which is parallel to the vector `2vec(a) - vec(b) + 3vec(c)`.

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The correct Answer is:
`2hat(i) - 4hat(j) + 4hat(k)`
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