Prove that if a plane has the intercepts a, b, c and is at a distance of P units from the origin, then

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Solution

The equation of a plane having intercepts a, b, c with x, y, and z axes respectively is given by,

The distance (p) of the plane from the origin is given by,

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Prove that if a plane has the intercepts a, b, c and if it is at a distance of p units from the origin, then $\frac{1}{a^{2}} + \frac{1}{b^{2}} + \frac{1}{c^{2}} = \frac{1}{p^{2}}$

Q. Prove that if a plane has the intercepts

a, b, c

and is at a distance of

p

unis from the origin then

\frac{1}{a^{2}} + \frac{1}{b^{2}} + \frac{1}{c^{2}} = \frac{1}{p^{2}}

Q. If a plane has the intercept

a, b, c

and is at a distance of

p

units from the origin then prove that

\frac{1}{a^{2}} + \frac{1}{b^{2}} + \frac{1}{c^{2}} = \frac{1}{p^{2}}

Q. Prove that if a plane has the intercepts a , b , c and is at a distance of P units from the origin, then

The line L has intercepts a and b on the coordinate axes. When keeping the origin fixed, the coordinate axes are rotated through a fixed angle, then the same line has intercepts p and q on the rotated axes. Then
(I.I.T. 1990)

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Prove that if a plane has the intercepts a, b, c and is at a distance of P units from the origin, then

The equation of a plane having intercepts a, b, c with x, y, and z axes respectively is given by, The distance (p) of the plane from the origin is given by,

The equation of a plane having intercepts a, b, c with x, y, and z axes respectively is given by,

The distance (p) of the plane from the origin is given by,