Find the equation of the plane with intercepts 2, 3 and 4 on the x,y and z axes respectively

Let the equation of plane be 

Find the equation of the plane with intercepts 2, 3 and 4 on the x,y and z axes respectively

Here a = 2,  b = 3, c = 4
∴    equation of plane is
                   
Find the equation of the plane with intercepts 2, 3 and 4 on the x,y and z axes respectively
      or      6x + 4y + 3z = 12
             

Find the equation of the plane with intercepts 2, 3 and 4 on the x,y and z axes respectively

Text Solution

Solution : It is given that the `x,y` and `z` intercepts of the plane are `2,3` and `4` respectively, i.e., <br> `a=2` <br> `b=3` <br> `c=4` <br> Now, it is known that the equation of a plane with intercepts `a,b` and `c` is given by, <br> `x/a+y/b+z/c=1` <br> Substituting the values of `a,b` and `c` in the above, <br> `x/2+y/3+z/4=1` <br> `=>(6xxx+4xxy+3xxz)/12=1` <br> `=>(6x+4y+3z)/12=1` <br> `=>(6x+4y+3z)/12xx12=1xx12` <br> `=>6x+4y+3z=12` <br> Which is the required equation of plane.

Last updated at Feb. 1, 2020 by

Find the equation of the plane with intercepts 2, 3 and 4 on the x,y and z axes respectively

Find the equation of the plane with intercepts 2, 3 and 4 on the x,y and z axes respectively

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Example 19 Find the equation of the plane with intercepts 2, 3 and 4 on the x, y and z-axis respectively. The equation of a plane with intercepts 𝑎, b, c on x, y, and z – axis respectively is 𝒙/𝒂 + 𝒚/𝒃 + 𝒛/𝒄 = 1 Given, Intercept on x − axis = 2 ∴ 𝑎 = 2 Intercept on y − axis = 3 ∴ b = 3 Intercept on z – axis = 4 ∴ c = 4 Equation of plane is 𝒙/𝟐 + 𝒚/𝟑 + 𝒛/𝟒 = 1 6𝑥/12 + 4𝑦/12 + 3𝑧/12 = 1 (6𝑥 + 4𝑦 + 3𝑧)/12 = 1 6x + 4y + 3z = 12