Home
Class 12
MATHS
Statement 1: let A( vec i+ vec j+ vec k)...

Statement 1: let `A( vec i+ vec j+ vec k)` and` B( 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 `A` and `B` are any two points and `P` is a point in space such that ` vec P A . vec P B >0` , then point `P` lies exterior to the sphere with `A B` as its diameter.

A

Statement I is true, Statement II is also true, Statement-II is the correct explanation of Statement-I.

B

Statement-I is true, Statement-II is also true, Statement-II is not the correct explanation of Statement-I.

C

Statement-I is true, Statement-II is false.

D

Statement-I is false, Statement -II is true.

Text Solution

Verified by Experts

The correct Answer is:
(d)
Promotional Banner

Similar Questions

Explore conceptually related problems

Statement 1: In "Delta"A B C , vec A B+ vec A B+ vec C A=0 Statement 2: If vec O A= vec a , vec O B= vec b ,t h e n vec A B= vec a+ vec b

Statement 1: | vec a|=3,| vec b|=a n d| vec a+ vec b|=5,t h e n| vec a- vec b|=5. Statement 2: The length of the diagonals of a rectangle is the same.

Statement 1: Let vec a , vec b , vec ca n d vec d be the position vectors of four points A ,B ,Ca n dD and 3 vec a-2 vec b+5 vec c-6 vec d=0. Then points A ,B ,C ,a n dD are coplanar. Statement 2: Three non-zero, linearly dependent coinitial vector ( vec P Q , vec P Ra n d vec P S) are coplanar. Then vec P Q=lambda vec P R+mu vec P S ,w h e r elambdaa n dmu are scalars.

Statement 1: if three points P ,Qa n dR have position vectors vec a , vec b ,a n d vec c , respectively, and 2 vec a+3 vec b-5 vec c=0, then the points P ,Q ,a n dR must be collinear. Statement 2: If for three points A ,B ,a n dC , vec A B=lambda vec A C , then points A ,B ,a n dC must be collinear.

If the position vector of a point A is vec a + 2 vec b and vec a divides AB in the ratio 2:3 , then the position vector of B, is

If vec(P) = (k,2,3) and vec(Q) = (0,3,k) and vec(P) bot vec(Q) , then find the value of k .

If vec c = 3vec a+4vec b and 2vec c =vec a -3vec b , show that (i) vec c and vec a have the same direction and |vec c| gt |vec a| (ii) vec b and vec c have opposite direction and |vec c| gt |vec b|

In a trapezium ABCD the vector B vec C = lambda vec(AD). If vec p = A vec C + vec(BD) is coillinear with vec(AD) such that vec p = mu vec (AD), then

If vec a , vec b are any two vectors, then give the geometrical interpretation of g relation | vec a+ vec b|=| vec a- vec b|

vec(a) and vec(b) are unit vectors and angle between them is pi/k . If vec(a)+2vec(b) and 5vec(a)-4vec(b) are perpendicular to each other then find the integer value of k.