The distance between the line vec r=2hat i-2hat j+3hat k+lambda (hat i-hat j+4hat k ) and the plane vec rcdot (hat i+5hat j+hat k )=5 is

3D Geometry: The distance between the line vec r=2hat i-2hat j+3hat k+lambda (hat… | AIEEE 2005

AIEEE 2005 (Offline)Question 1

The distance between the line $\vec r=2\hat i-2\hat j+3\hat k+\lambda\left(\hat i-\hat j+4\hat k\right)$ and the plane $\vec r\cdot\left(\hat i+5\hat j+\hat k\right)=5$ is

3D Geometry

$\frac{10}{9}$$\frac{10}{3\sqrt3}$✓ Correct answer$\frac{3}{10}$$\frac{10}{3}$

Solution

The line is parallel to the plane ($1-5+4=0$). Distance of $(2,-2,3)$: $\frac{|2-10+3-5|}{\sqrt{27}}=\frac{10}{3\sqrt3}$.

3D Geometry - JEE Mathematics question (AIEEE 2005 (Offline))

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