Question Video: Finding the Equation of a Plane Mathematics

Find the equation of the plane whose π₯-, π¦-, and π§-intercepts are β7, 3, and β4, respectively.

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Video Transcript

Find the equation of the plane whose π₯-, π¦-, and π§-intercepts are negative seven, three, and negative four, respectively.

In this question, weβre asked to find the equation of a plane. And to do this, weβre given that it has an π₯-intercept at negative seven, a π¦-intercept at three, and its π§-intercept is at negative four. And we can recall we know how to find the equation of a plane from its intercepts by using the intercept form of the equation of a plane. This tells us if the π₯-, π¦-, and π§-intercepts of a plane are π, π, and π for nonzero values, then π₯ over π plus π¦ over π plus π over π§ is equal to one is the equation of this plane. And since the three intercepts weβre given are nonzero, we can just substitute these values into our equation for the plane

We substitute π is equal to negative seven, π is equal to three, and π is equal to negative four into our intercept equation of the plane. We get π₯ over negative seven plus π¦ over three plus π§ over negative four is equal to one. We can then simplify this slightly. In the first and third term on the left-hand side of our equation, we can bring the factor of negative one into the expression. This gives us the following equation. And itβs worth noting we could write the coefficients of π₯, π¦, and π§ as integers by multiplying the equation through by 84. However, we can just leave our answer in this form. This gives us the answer of negative π₯ over seven plus π¦ over three minus π§ over four is equal to one.