A plane P passes through the line of intersection of the planes `2x -y +3z = 2, x + y - 2 =1` and the point `(1, 0, 1).` What are the direction ratios of the line of intersection of the given planes? What is the equation of the plane P? If the plane P touches the sphere `x^2 + y^2 + z^2 = r^2,` then what is `r` equal to?

Options

A. `2/sqrt29`
B. `4/sqrt29`
C. `5/sqrt29`
D. 1

Answer

C

Explanation

Plane P touches the sphere `x^2+y^2+z^2=r^2` then r = Distance between centre of sphere (0,0,0) to plance P.
`rArr r=abs((5(0)+2(0)-5)/sqrt(5^2+2^2+(0)^2))`
`=5/sqrt(25+4)`
`r=5/sqrt29`