Question

The plane $x+y+z=5\sqrt{3}$ and sphere $x^2+y^2+z^2=5$

• A. touch each other
• B. cut in a circle
• C. do not meet
• D. none of these

Answer 1

Answer: (A)

touch each other

Distance of plane $x+y+z=5\sqrt{3}$ from the centre $(0,0,0)$ of sphere $x^2+y^2+z^2=5$

$=\frac{|-5\sqrt{3}|}{\sqrt{1^2+1^2+1^2}}=5$ (radius of sphere), so plane touches it.