Question

Determine the area of the triangle formed by the x, y and z-intercepts of the plane 2x - 3y + 5z = 60.

Answer 1

my calc's a little rusty but I hope I can answer this properly

step 1: find the x, y, and z, intercepts. to find the x intercept, let y and z = 0 and solve for x. similarly, for y-intercept, let x and z = 0 and solve for y. same process for the z-intercept

step 2: sketch the intercepts, then find adjacent vectors (ex. vector AB and AC, which you would determine by subtracting B-A and C-A respectively)

step 3: cross-product of the vectors using the 3x3 determinant method. let me know if you need me to explain this to you, here's a link that may help: https://tutorial.math.lamar.edu/classes/calcII/CrossProduct.aspx)

step 4: take the magnitude of the resulting vector from step 3. then divide by 2 (the magnitude of the vector is actually the area of the paralellogram formed by the two vectors, so we divide by 2 to get the triangle)