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Statement 1: let A( vec i+ vec j+ vec k)...

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.

Text Solution

Verified by Experts

The correct Answer is:
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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