To find the equation of a plane given its intercepts on the x, y, and z axes, we can use the intercept form of the equation of a plane. The general form is:
1/x + 1/y + 1/z = 1
Where:
- x-intercept = 2
- y-intercept = 3
- z-intercept = 1
Substituting the intercept values into the equation:
1/2 + 1/3 + 1/1 = 1
To combine these fractions, we first find a common denominator, which is 6:
3/6 + 2/6 + 6/6 = 1
This simplifies to:
11/6 = 1
Now, we can write the equation of the plane:
(x/2) + (y/3) + (z/1) = 1
To tidy it up, we can multiply through by 6 to eliminate the fractions:
3x + 2y + 6z = 6
Thus, the equation of the plane is:
3x + 2y + 6z = 6