The value of - for which the plane x- y-z-5 cuts equal intercepts on the axes- is

Equation of a plane which equal intercept on the axes is xa+4a+za=1 Since x + alpha;y + z = 5 cuts equal intercept i.e. #160;x5+ #945;5y+z5=1i.e. #160; ...

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Standard XII

Mathematics

Equation of a Plane : Intercept Form

The value of ...

Question

The value of $α$ for which the plane x + $α y$ + z = 5 cuts equal intercepts on the axes, is ____________.

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Solution

Equation of a plane which equal intercept on the axes is $\frac{x}{a} + \frac{4}{a} + \frac{z}{a} = 1$
Since x + αy + z = 5 cuts equal intercept
$i . e . \frac{x}{5} + \frac{α}{5} y + \frac{z}{5} = 1 i . e . \frac{1}{5} = \frac{α}{5} i . e . α = 1$

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The value of α for which the plane x + αy + z = 5 cuts equal intercepts on the axes, is ____________.

Equation of a plane which equal intercept on the axes is xa+4a+za=1 Since x + αy + z = 5 cuts equal intercept i.e. x5+α5y+z5=1i.e. 15=α5i.e. α=1

The value of $α$ for which the plane x + $α y$ + z = 5 cuts equal intercepts on the axes, is ____________.

Equation of a plane which equal intercept on the axes is $\frac{x}{a} + \frac{4}{a} + \frac{z}{a} = 1$
Since x + αy + z = 5 cuts equal intercept
$i . e . \frac{x}{5} + \frac{α}{5} y + \frac{z}{5} = 1 i . e . \frac{1}{5} = \frac{α}{5} i . e . α = 1$