Mathematics · Vector Algebra
Let vector AB = i + 2j + 2k and vector AC = ai + bj - 3k, where a, b ∈ &mathbb;Z. A point D lies on BC such that its perpendicular distances from the lines AB and AC are equal. If |vector AC| = 7 and vector AD = 2i + j + k, then find the value of 3a - 2b.
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