Q48 / 100 · NTA Abhyas (JEE Main) 2020 · Mathematics · Vector Algebra

If for a plane, $x, y, z$ intercepts are $8, 4, 4$ respectively, then the length of the perpendicular from the origin on to the plane is

Correct answer
A
$\frac{8}{3}$ units
B
$\frac{3}{8}$ units
C
$3$ units
D
$\frac{4}{5}$ units

Solution

Equation of plane is

\frac{x}{8} + \frac{y}{4} + \frac{z}{4} = 1

\Rightarrow x + 2 y + 2 z = 8

Length of perpendicular from origin to

x + 2 y + 2 z - 8 = 0

= |\frac{- 8}{\sqrt{1 + 4 + 4}}| = \frac{8}{3}

Hence, the correct answer is option: 'A'.

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