Problem 11

Question

Find the intercepts and sketch the graph of the plane. $$ x+y-z=0 $$

Step-by-Step Solution

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Answer

The x-intercept, y-intercept, and z-intercept of the plane equation $x+y-z=0$ are all at the origin (0, 0, 0). The graph of this plane is a plane passing through the origin, cutting the x, y, and z axes at this point.

1Step 1: Finding the X-intercept

For the x-intercept, set y and z equals to zero in the equation. You're left with $x=0$. Thus, the x-intercept is at the point (0, 0, 0).

2Step 2: Finding the Y-intercept

For the y-intercept, set x and z equals to zero in the equation. You will be left with $y = 0$. Thus, the y-intercept is at the point (0, 0, 0).

3Step 3: Finding the Z-intercept

For the z-intercept, set x and y equals to zero in the equation. You will be left with $-z = 0$, which simplifies to $z=0$. Thus, the z-intercept is at the point (0, 0, 0).

4Step 4: Sketching the graph

All intercepts are at the origin (0,0,0). The graph will be a plane passing through the origin. It will slice all three coordinate axes at the origin.

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