Home
Class 12
MATHS
If veca & vecb are the position vectors ...

If `veca` & `vecb` 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:

A

(a) `3veca-vecb`

B

(b) `3vecb-veca`

C

(c) `3veca-2vecb`

D

(d) `3vecb-2veca`

Text Solution

Verified by Experts

The correct Answer is:
D
Since, given that AC=3AB. It means that point C divides AB externally.
Thus, `AC:BC=3:2`

Hence, `OC=(3*b-2*a)/(3-2)=3b-2a`
Promotional Banner

Topper's Solved these Questions

  • VECTOR ALGEBRA

    ARIHANT MATHS|Exercise Exercise For Session 1|7 Videos

  • VECTOR ALGEBRA

    ARIHANT MATHS|Exercise Exercise For Session 2|17 Videos

  • TRIGONOMETRIC FUNCTIONS AND IDENTITIES

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|18 Videos

Similar Questions

Explore conceptually related problems

If vec a and vec b are the position vectors of A and B respectively, find the position vector of a Point C in BA produced such that BC = 1.5 BA.

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

The position vector of a point C with respect to B is hat i +hat j and that of B with respect to A is hati-hatj . The position vector of C with respect to A is

If the position vectors of A and B respectively hati+3hatj-7hatk and 5 hati-2hatj+4hatk , then find AB

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 and B are the points (-3,4) and (2, 1), then the coordinates of the point C on AB produced such that AC-2BC are

If veca,vecb,vecc are the position vectors of the vertices A,B,C of a /_\ABC respectively, find an expression for the area of /_\ABC and hence deduce the condition for the points A,B,C to be collinear.

If the position vectors of the points A and B are hati+3hatj-hatk and 3hati-hatj-3hatk , then what will be the position vector of the mid-point of AB

The position vectors of vertices of DeltaABC are a,b,c and a*a=b*b=c*c=3. if [a b c]=0, then the position vectors of the orthocentre of DeltaABC is

If a,b and c are the position vectors of the vertices A,B and C of the DeltaABC , then the centroid of DeltaABC is