(1, 3, 5)

Sol. Any point on the line = = k (say) ...(1)

is P(k, 2k + 1, 3k + 2)

Let it be the foot of from Q(1, 6, 3) on the line (1)

Then d.r.s. of PQ are k – 1, 2k + 1 – 6, 3k + 2 – 3 i.e., k – 1, 2k – 5, 3k – 1

As PQ is to the line (1), so

(k – 1) × 1 + (2k – 5) × 2 + (3k – 1) × 3 = 0 ⇒ k – 1 + 4k – 10 + 9k – 3 = 0 ⇒ 14k – 14 = 0 ⇒ k = 1.

∴ The foot of the is given by P(1, 2 × 1 + 1, 3 × 1 + 2) = (1, 3, 5).

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