एक त्रिभुज ABC में, यदि |vec(BC)|=8, |vec(CA)|=7, |vec(AB)|=10, तो vec(AB) का प्रक्षेपण...

In a triangle ABC, if |vec(BC)|=8, |vec(CA)|=7, |vec(AB)|=10 , then the projection of the vec(AB) on vec(AC) is equal to :

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) .

Assertion A : If A, B, C, D are four points on a semi-circular arc with centre at 'O' such that |vec(AB)| = |vec(BC)|=|vec(CD)| , then vec(AB) +vec(AC) +vec(AD) =4 vec(AO) +vec(OB) +vec(OC) Reason R : Polygon law of vector addition yields vec(AB) +vec(BC) +vec(CD) +vec(AD)=2vec(AO) In the light of the above statements, choose the most appropriate answer from the options given below :

State whether the following relations are true or false (1) vec(AB)=vec(BA) (2) vec(AB)=-vec(BA) (3) |vec(AB)|=|vec(BA)| (4) |vec(AB)|=|-vec(AB)| (5) hatj=hatk (6) |hatj|=|hatk|

Assertion: If I is the incentre of /_\ABC, then |vec(BC)|vec(IA)+|vec(CA)|vec(IB)+|vec(AB)|vec(IC)=0 Reason: If O is the origin, then the position vector of centroid of /_\ABC is (vecOA)+vec(OB)+vec(OC))/3 (A) Both A and R are true and R is the correct explanation of A (B) Both A and R are true R is not te correct explanation of A (C) A is true but R is false. (D) A is false but R is true.

In a triangle ABC, if taken in order, consider the following statements 1. vec(AB) + vec(BC) + vec(CA) = vec(0) 2 vec(AB) + vec(BC) - vec(CA) = vec(0) 3. vec(AB)- vec(BC) + vec(CA) = vec(0) 4. vec(BA)- vec(BC) + vec(CA) = vec(0) How many of the above statements are correct?

In a quadrilateral ABCD, vec(AB) + vec(DC) =

In a triangle ABC if vecabs(AB)=7 ,vecabs(BC)=5 ,and vecabs(CA)=3. . If the projection of vec(BC) on vec(CA) is n/2 , then the value of n is