 Hi, and welcome to the session. Let's work out the following question. The question says if the plane x plus y plus z equals to square root 3 lambda touches the square x square plus y square plus z square minus 2x minus 2y minus 2z minus 6 equals to 0, find the value of lambda. So, let us see the solution to this question. The square is x square plus y square plus z square minus 2x minus 2y minus 2z minus 6 equals to 0. Therefore, the center 1, 1, 1 and radius will be equal to square root 1 plus 1 plus 1 plus 6 that is equal to square root of 9 that is equal to 3. Let us name this 1. Now, the equation of plane is x plus y plus z minus square root 3 lambda is equal to 0. This we call equation 2. Now, as plane 2 touches the square then mod of perpendicular from center of square to plane should be equal to radius. This implies mod of x plus y plus z minus square root 3 lambda divided by square root of 1 square plus 1 square plus 1 square at the point or from the point c that is 1, 1, 1 is equal to 3. This implies 1 plus 1 plus 1 minus square root 3 lambda divided by square root 3 in the mod is equal to 3. This implies 3 minus square root 3 lambda divided by square root 3 is equal to plus minus 3. This implies 3 minus square root 3 lambda is equal to plus minus 3 root 3. Hence, lambda is equal to square root 3 plus minus 3. So, this is our answer to this question. I hope that you understood the solution and enjoyed the session. Have a good day.