What is the length of the perpendicular drawn from point (3, 4, 5) to line ?

Question

Question

This question was previously asked in

AAI ATC Junior Executive 21 Feb 2023 Shift 2 Official Paper

Answer 1

Given:

Line and point (3, 4, 5)

Concept:

If two vectors are perpendicular to each other then dot product of both is zero.

Calculation:

Let point A = (3, 4, 5)

and

Then point B = (k, 2k + 1, 3k + 2) on the line

Now, the line AB = B - A = (k - 3, 2k - 3, 3k - 3) .

DRs of given line (1, 2, 3)

We know that the Line AB is perpendicular to the given line

Then

(k - 3, 2k - 3, 3k - 3) ⋅ (1, 2, 3) = 0

⇒ k - 3 +4k - 6 + 9k - 9 = 0

⇒ 14k = 18 ⇒

Then line

The perpendicular length from point A on given line is the magnitude of AB.

Hence option (2) is correct.

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