Problem 5
Question
Find the intercepts and sketch the graph of the plane. $$ 2 x-y+3 z=4 $$
Step-by-Step Solution
Verified Answer
The x-intercept is at (2,0,0), the y-intercept is at (0,-4,0), and z-intercept is at (0,0,4/3).
1Step 1: Find the x-intercept
The x-intercept can be found by setting y and z to 0 in the equation. This gives the equation as \(2x - 0 + 3*0 = 4\), which simplifies to \(2x = 4\). Solving this equation yields the x-intercept. \(x = 4/2 =2\).
2Step 2: Find the y-intercept
To find the y-intercept, set x and z to 0. This gives the equation as \(2*0 - y + 3*0 = 4\), which simplifies to \(-y = 4\). Solving for y, we get \(y = -4\).
3Step 3: Find the z-intercept
To find the z-intercept, set x and y to 0 in the equation. This gives \(2*0 - 0 + 3z = 4\), which simplifies to \(3z = 4\). Solving for z we get \(z = 4/3\).
4Step 4: Plot the intercepts and the plane
Plot the intercepts on the x, y, z axes at points (2,0,0), (0,-4,0), and (0,0,4/3). Then, sketch the plane that connects these points. This gives you a visual representation of the equation for the plane.
Other exercises in this chapter
Problem 5
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