Home
Class 12
MATHS
A, B, C, D are any four points, then vec...

A, B, C, D are any four points, then `vec(AB).vec(CD)+vec(BC).vec(AD)+vec(CA).vec(BD)`=

A

`2 vec(AB).vec(BC).vec(CD)`

B

`vec(AB)+vec(BC)+vec(CD)`

C

`5 sqrt3`

D

0

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Similar Questions

Explore conceptually related problems

If A,B,C,D are four points in space, then |vec(AB)xvec(CD)+vec(BC)xxvec(AD)+vec(CA)xxvec(BD)|=k (are of /_\ABC) where k= (A) 5 (B) 4 (C) 2 (D) none of these

If A,B,C,D are any four points in space prove that vec(AB)xxvec(CD)+vec(BC)xvec(AD)+vec(CA)xxvec(BD)=2vec(AB)xxvec(CA)

A,B,C,D are any four points,prove that vec AB*vec CD+BC*vec AD+vec CA*vec BD=0

In a right angled triangle ABC, the hypotenuse AB =p, then vec(AB).vec(AC) + vec(BC).vec(BA)+vec(CA).vec(CB) is equal to:

For any four points A,B,C,D |vec (AB) xx vec (CD)-vec (BC) xx vec (AD)+vec (CA) xx vec (BD)| is equal to 4 times the area of triangle- (1) ABC (2) BCD (3) ACD (4) ABD

In a right angled triangle hypotenuse AC= p, then vec(AB). vec(AC ) + vec(BC) .vec(BA) + vec(CA). vec(CB) equal to ?

ABCDE is a pentagon prove that vec(AB)+vec(BC)+vec(CD)+vec(DE)+vec(EA)=vec0

If D E and F be the mid ponts of the sides BC, CA and AB respectively of the /_\ABC and O be any point, then prove that vec(OA)+vec(OB)+vec(OC)=vec(OD)+vec(OE)+vec(OF)

A, B, C, D are four points in the space and satisfy |vec(AB)|=3, |vec(BC)|=7, |vec(CD)|=11 and |vec(DA)|=9 . Then find the value of vec(AC)*vec(BD) .