Question

Find the direction ratios of the normal to the plane, which passes through the points (1, 0, 0) and (0, 1, 0) and makes angle \(\frac{\pi}{4}\) with the plane x + y = 3. Also find the equation of the plane.

Answer 1

Let the equation of plane passing through the point (1, 0, 0) be

Since, (i) also passes through (0, 1, 0)

Given the angle between plane (i) and plane x + y = 3 is \(\frac{\pi}{4}.\)

Now, equation (i) becomes

\(ax+ay\pm\sqrt{2}az=a\)

\(\Rightarrow x+y\pm\sqrt{2}z=1,\) is the required equation of plane.

Therefore, required direction ratios are 1, 1, \(\pm \sqrt{2}.\)