Question

The equation of plane which cuts equal intercepts of unit length on the coordinate axes is:

• A. x+y+z=3
• B. x+y-z=1
• C. x+y+z=1
• D. x+y+z=0

Answer 1

The Correct Option is C

The equation of a plane in three-dimensional space that cuts off equal intercepts of length 1 on the coordinate axes is determined by setting the intercept form of the plane equation:

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

Here, \(a\), \(b\), and \(c\) are the intercepts on the \(x\), \(y\), and \(z\) axes, respectively. For equal intercepts of unit length, we have \(a = b = c = 1\).

Substituting these values into the intercept form gives:

\( \frac{x}{1} + \frac{y}{1} + \frac{z}{1} = 1 \)

Simplifying this, we obtain:

\( x + y + z = 1 \)

Therefore, the equation of the plane that cuts equal intercepts of unit length on each of the coordinate axes is \( x + y + z = 1 \).

The correct answer is the option: x+y+z=1.