Question

Assertion (A) : If the spheres $x^2+y^2+z^2=64$ & $x^2+y^2+z^2-12x+4y-6z+48=0$ touch externally
Reason (R) : If the distance between the centres of spheres is equal to the sum of their radii, then they touch externally

• A. Both (A) & (R) are individually true & (R) is correct explanation of (A)
• B. Both (A) & (R) are individually true but (R) is not the correct (proper) explanation of (A)
• C. (A) is true but (R) is false
• D. (A) is false but (R) is true

Answer 1

Answer: (D)

$\because C_1\equiv (0,0,0),r_1=8$
$C_2\equiv \left(6,-2,3\right),r_2=\sqrt{36+4+9-48}=1$
As $C_1{C}_2=\sqrt{36+4+9}=7$ & $\left|r_1-r_2\right|=7$
$\Rightarrow C_1{C}_2=\left|r_1-r_2\right|=7$
$\Rightarrow$ Spheres touches internally
$\Rightarrow$ Assertion (A) is false but Reason (R) is true