If the direction ratios of the normal to a plane are lt l, m, n gt and the length of the normal is p, then what is the sum of intercepts cut-off by the plane from the coordinate axes?

Options

A. `p(1/l+1/m+1/n)`
B. `psqrt((l^2+m^2+n^2))`
C. `psqrt((l^2+m^2+n^2))(1/l+1/m+1/n)`
D. `p/sqrt((l^2+m^2+n^2))(1/l+1/m+1/n)`

Answer

A

Explanation

Since, the direction ratio's of normal to a plane are ltl,m,ngt and the length of normal is p, then intercept on x-axis p/l and that on y-axis is p/m and on z-axis it is p/n, hence su of intercepts cut off by the plene from the coordinate axes
`=p(1/l+1/m+1/n)`