Statement 1: let `A( vec i+ vec j+ vec k)a n dB( vec i- vec j+ vec k)` be two points. Then point `P(2 vec i+3 vec j+ vec k)` lies exterior to the sphe

Monjur Alahi

Statement 1: let `A( vec i+ vec j+ vec k)a n dB( vec i- vec j+ vec k)` be two points. Then point `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.


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Salim Ahmed Kawsar

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Correct Answer - b
`vec(PA)*vec(PB)= 9 gt 0`. Therefore, P is exterior to the sphere. Statement 2 is also true (standard result).

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