The distance of the origin (0, 0, 0) from the plane -2x + 6y - 3z = -7 is:

Question

The distance of the origin (0, 0, 0) from the plane $- 2 x + 6 y - 3 z = - 7$ is:

Smart Achievers · Accepted Answer

(1)

Ans. 1 unit

Explanation:

$Given, equation of plane is$

$- 2 x + 6 y - 3 z = - 7$

$\Rightarrow$ $- 2 x + 6 y - 3 z + 7 = 0$

$We know distance of point (x_{1}, y_{1}, z_{1}) from a plane A x + B y + C z + D = 0 is given as$

$Distance =$ $| \frac{A x_{1} + B y_{1} + C z_{1} + D}{\sqrt{A^{2} + B^{2} + C^{2}}} |$

$∴$ $Distance =$ $| \frac{- 2 (0) + 6 (0) + (- 3) (0) + 7}{\sqrt{4 + 36 + 9}} |$

$=$ $| \frac{7}{\sqrt{49}} |$ $=$ $| \frac{7}{7} |$ $= 1 unit$

Want Us to Email you About Special Offers & Updates?