`A B C D E` is pentagon, prove that ` vec A B` + ` vec B C` + ` vec C D` + ` vec D E+ vec E A` = ` vec0` ` vec A B+ vec A E+ vec B C+ vec D C+ vec E D+ vec A C=3 vec A C`

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

The position vectors of A, B,C and D are vec a , vec b , vec 2a+ vec 3b and vec a - vec 2b respectively. Show that vec (DB)=3 vec b -vec a and vec (AC) =vec a + vec 3b

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

' I ' is the incentre of triangle A B C whose corresponding sides are a , b ,c , rspectively. a vec I A+b vec I B+c vec I C is always equal to a. vec0 b. (a+b+c) vec B C c. ( vec a+ vec b+ vec c) vec A C d. (a+b+c) vec A B

If the lines vec r = vec a + lambda (vec b xx vec c) and vec r = vec b + mu (vec c xx vec a) are intersect then ...............

The non-zero vectors are vec a,vec b and vec c are related by vec a= 8vec b and vec c = -7vec b . Then the angle between vec a and vec c is

The non-zero vectors are vec a,vec b and vec c are related by vec a= 8vec b and vec c = -7vec b . Then the angle between vec a and vec c is

vec a , vec b , vec c are three coplanar unit vectors such that vec a+ vec b+ vec c=0. If three vectors vec p , vec q , and vec r are parallel to vec a , vec b , and vec c , respectively, and have integral but different magnitudes, then among the following options, | vec p+ vec q+ vec r| can take a value equal to

If A=(0,1)B=(1,0),C=(1,2),D=(2,1) , prove that vec A B= vec C Ddot

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|