Question

Consider the points closest to the origin on the planes x + y + z = a.

(a) The closest point travels farther as a  is increased

(b) The closest point travels nearer as a  is increased

(c) The closest point is independent of a as a is not there in the expression of the gradient.

(d) Varies as a^2, away from the origin.

This question was posed to me in final exam.

Question is from Lagrange Method of Multiplier to Find Maxima or Minima topic in chapter Maxima and Minima of Engineering Mathematics

Answer 1

The correct answer is (a) The closest point travels farther as a  is increased

Easiest explanation: The intercept of the planes increase as we increase the a value. Hence, we may conclude that the closest point of lower a value plane would be closer to the origin. The Lagrange multiplier set up can be used to verified this.