Home
Class 12
MATHS
A,B,C and D have position vectors a,b,c ...

A,B,C and D have position vectors a,b,c and d, respectively, such that a-b=2(d-c). Then,

A

AB and CD bisect each other

B

BD and AC bisect each other

C

AB and CD trisect each other

D

BD and AC trisect each other

Text Solution

Verified by Experts

The correct Answer is:
D
`a-b=2(d-c)`
`therefore(a+2c)/(2+1)=(b+2d)/(2+1)`
Hence, AC and BD trisect each other as LHS is the position vector of a point trisecting A an C, and RHS that of B and D.
Promotional Banner

Similar Questions

Explore conceptually related problems

Recognise a,b,c, and d.

If vec a , vec b , vec c , vec d are the position vector of point A , B , C and D , respectively referred to the same origin O such that no three of these point are collinear and vec a + vec c = vec b + vec d , than quadrilateral A B C D is a ;

If position vector of points A,B and C are respectively hati,hatj, and hatk and AB=CX , then position vector of point X is

If a,b are the position vectors of A,B respectively and C is a point on AB produced such that AC=3AB then the position vector of C is

If the position vectors of the points A,B and C be a,b and 3a-2b respectively, then prove that the points A,B and C are collinear.

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

Find out the shift in point B, C and D

If D ,Ea n dF are three points on the sides B C ,C Aa n dA B , respectively, of a triangle A B C such that AD,BE and CF are concurrent, then show that (B D)/(C D),(C E)/(A E),(A F)/(B F)=-1

The position vectors of two points A and B are respectively 6vec(a)+2vec(b) and vec(a)-3bar(b) . If the point C divides AB internally in the ratio 3 : 2 then the position vector of C is ……………

Let A,B,C,D,E represent vertices of a regular pentangon ABCDE. Given the position vector of these vertices be a,a+b,b, lamda a and lamdab respectively. Q. AD divides EC in the ratio