Question

Find the equation of the plane whose intercept on $x,y,z$ axes $1,2,4$ respectively

Answer 1

Equation of plane with intercepts $a,b$ and $c$ on $x,y$ and $z$-axis respectively is given as-

$\frac{x}{a}+\frac{y}{b}+\frac{z}{c}=1$

Now,

Intercept on $x$-axis $\left(a\right)=1$

Intercept on $y$-axis $\left(b\right)=2$

Intercept on $z$-axis $\left(c\right)=4$

Therefore,

Equation of plane-

$\frac{x}{1}+\frac{y}{2}+\frac{z}{4}=1$

$\frac{4x+2y+z}{4}=1$

$\Rightarrow 4x+2y+z=4$

Hence the equation of plane whose intercept on $x,y$ and $z$-axis are $1,2$ and $4$ respectively is-

$4x+2y+z=4$