Q3 of 230 Page 30

Find the equation of a plane which meets the axes in A, B and C, given that the centroid of the triangle ABC is the point (α, β, γ).

It is given in the question that the plane meets the axes in A, B, C


So now let us assume that A = (a, 0, 0), B = (0, b, 0) and C = (0, 0, c)


Given that the centroid is and we know the formula of the centroid of



So,




So we have now





We know that, The equation of the plane whose intercepts on the coordinate axes a, b, c is given by the equation



Now substitute a, b, c


We get



so this is the equation.


More from this chapter

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2

Reduce the equations of the following planes in the intercept form and find its intercepts on the coordinate axes:

2x + 3y – z = 6

 2

Reduce the equations of the following planes in the intercept form and find its intercepts on the coordinate axes:

2x – y + z = 5

 4

Find the equation of the plane passing through the point (2, 4, 6) and making equal intercepts of the coordinate axes.

 5

A plane meets the coordinate axes at A, B and C respectively such that the centroid of the triangle ABC is (1, – 2, 3). Find the equation of the plane.