Statement 1: let `A( vec i+ vec j+ vec k)a n dB( vec i- vec j+ vec k)`be two points. Thenpoint `P(2 vec i+3 vec j+ vec k)`lies exterior to the sphere with `A B`as its diameter.Statement 2: If `Aa n dB`are any two points and `P`is a point in space such that ` vec P Adot vec P B >0`, then point `P`lies exterior to the sphere with `A B`as its diameter.A. Both the statements are true, and Statement 2 is the correct explanation for Statement 1.B. Both the Statements are true, but Statement 2 is not the correct explanation for Statement 1.C. Statement 1 is true and Statement 2 is false.D. Statement 1 is false and Statement 2 is true.

Statement 1: let `A( vec i+ vec j+ vec k)a n dB( vec i- vec j+ vec k)`

1.	Statement 1: let `A( vec i+ vec j+ vec k)a n dB( vec i- vec j+ vec k)`be two points. Thenpoint `P(2 vec i+3 vec j+ vec k)`lies exterior to the sphere with `A B`as its diameter.Statement 2: If `Aa n dB`are any two points and `P`is a point in space such that ` vec P Adot vec P B >0`, then point `P`lies exterior to the sphere with `A B`as its diameter.A. Both the statements are true, and Statement 2 is the correct explanation for Statement 1.B. Both the Statements are true, but Statement 2 is not the correct explanation for Statement 1.C. Statement 1 is true and Statement 2 is false.D. Statement 1 is false and Statement 2 is true.
Answer» Correct Answer - b `vec(PA)*vec(PB)= 9 gt 0`. Therefore, P is exterior to the sphere. Statement 2 is also true (standard result).