JEE Main · 2018 · 08 Apr 2018 · Offline · Three Dimensional Geometry

The length of the projection of the line segment joining the points

(5, - 1, 4)

and

(4, - 1, 3)

on the plane,

x + y + z = 7

is :

(A) $\frac{2}{3}$ ✓ Correct
(B) $\frac{2}{3}$
(C) $\frac{2}{3}$
(D) $\frac{1}{3}$

Answer: (A)

Solution

The segment joining

(5, - 1, 4)

and

(4, - 1, 3)

has direction

(1, 0, 1)

and length

2

, while the plane

x + y + z = 7

has normal

(1, 1, 1)

. The angle

θ

the segment makes with the normal satisfies

cos θ = \frac{∣1 + 0 + 1∣}{2 \cdot 3} = \frac{2}{6}

, so its projection onto the plane is

2 sin θ = 2 1 - \frac{4}{6} = 2 \cdot \frac{1}{3} = \frac{2}{3}

JEE Main · 2018 · 08 Apr 2018 · Offline · Single correct option

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