If a plane passes through the point (1, 1, 1) and is perpendicular to the line x - $\frac{1}{3}$ = y - $\frac{1}{0}$ = z - $\frac{1}{4}$ then its perpendicular distance from the origin is ______.

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If a plane passes through the point (1, 1, 1) and is perpendicular to the line x - $\frac{1}{3}$ = y - $\frac{1}{0}$ = z - $\frac{1}{4}$ then its perpendicular distance from the origin is underlinebb($\frac{7}{5}$). Explanation: Since the plane is perpendicular to the given line, its direction ratios are proportional to 3, 0, 4 So, the required equation of the plane is of the form 3x + 0y + 4z + d = 0 ... \left( 1 \right), \text{where d is a constant}. \text{Since this plane passes through} (1, 1, 1), 3 + 0 + 4 + d = 0 \Rightarrow d = - 7 \text{Substituting this in (1), we get} 3x + 0y + 4z - 7 = 0 ... \left( 2 \right) \text{Perpendicular distance of (2) from the origin} = \frac{\left|3\left(0\right) + 0 + 4 \left(0\right) - 7 \right|}{$\sqrt$(3^2 + 0^2 + 4^2)} = \frac{\left| 0 + 0 - 7 \right|}{$\sqrt$(25)} = $\frac{7}{5}$ \text{units}

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