JEE Main · 2020 · 09 Jan 2020 · Shift 1 · Three Dimensional Geometry

The projection of the line segment joining the points

(1, - 1, 3)

and

(2, - 4, 11)

on the line joining the points

(- 1, 2, 3)

and

(3, - 2, 10)

is ______

Answer: 8

Solution

The segment joins

A (1, - 1, 3)

B (2, - 4, 11)

, so

A B = \hat{i} - 3 \hat{j} + 8 \hat{k}

. The line's direction, from

(- 1, 2, 3)

(3, - 2, 10)

, is

C D = 4 \hat{i} - 4 \hat{j} + 7 \hat{k}

, of length

16 + 16 + 49 = 9

. The projection is

\frac{A B \cdot C D}{∣ C D ∣} = \frac{4 + 12 + 56}{9} = \frac{72}{9} = 8

JEE Main · 2020 · 09 Jan 2020 · Shift 1 · Integer answer

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