The length of the projection of the line segment joining the points and on the plane, is
- A.
- B.
- C.
- D.
Show answer and solution
Correct option: D
Solution
The line segment has direction vector d = (4-5, -1-(-1), 3-4) = (-1, 0, -1), with length |d| = √2.
The plane normal is n = (1,1,1)/√3. The component of d along n is d·n̂ = (-1+0-1)/√3 = -2/√3, so its magnitude is 2/√3.
The projection length onto the plane uses: projection² = |d|² - (d·n̂)² = 2 - 4/3 = 2/3.
Therefore the projection length = √(2/3).
The plane normal is n = (1,1,1)/√3. The component of d along n is d·n̂ = (-1+0-1)/√3 = -2/√3, so its magnitude is 2/√3.
The projection length onto the plane uses: projection² = |d|² - (d·n̂)² = 2 - 4/3 = 2/3.
Therefore the projection length = √(2/3).
[JEE Main 2018]