Home
Class 12
MATHS
Let A,B,C be vertices of a triangle ABC ...

Let A,B,C be vertices of a triangle ABC in which B is taken as origin of reference and position vectors of A and C are `veca and vecc` respectively. A line AR parallel to BC is drawn from A PR (P is the mid point of AB) meets AC and Q and area of triangle ACR is 2 times area of triangle ABC Position vector of R in terms `veca and vecc` is (A) `veca+2vecc` (B) `veca+3vecc` (C) `veca+vecc` (D) `veca+4vecc`

A

`vec(a)+2vec( c )`

B

`vec(a)+3vec( c )`

C

`vec(a)+vec( c )`

D

`vec(a)+4vec( c )`

Text Solution

Verified by Experts

The correct Answer is:
A
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • MATHEMATICS TIPS

    FIITJEE|Exercise PARAGRAPH BASED (MULTIPLE CHOICE) (COMPREHENSION-II)|3 Videos

  • MATHEMATICS TIPS

    FIITJEE|Exercise PARAGRAPH BASED (MULTIPLE CHOICE) (COMPERHENSION - III)|3 Videos

  • MATHEMATICS TIPS

    FIITJEE|Exercise MCQ (MULTIPLE CORRECT)|30 Videos

  • MATHEMATICS

    FIITJEE|Exercise NUMERICAL DECIMAL BASED QUESTIONS|15 Videos

  • MATRICES

    FIITJEE|Exercise NUMERICAL BASED|3 Videos

Similar Questions

Explore conceptually related problems

Let A,B,C be vertices of a triangle ABC in which B is taken as origin of reference and position vectors of A and C are veca and vecc respectively. A line AR parallel to BC is drawn from A PR (P is the mid point of AB) meets AC and Q and area of triangle ACR is 2 times area of triangle ABC Positon vector of Q for position vector of R in (1) is (A) (2veca+3vecc)/5 (B) (3veca+2vecc)/5 (C) (veca+2vecc)/5 (D) none of these

Let A,B,C be vertices of a triangle ABC in which B is taken as origin of reference and position vectors of A and C are veca and vecc respectively. A line AR parallel to BC is drawn from A PR (P is the mid point of AB) meets AC and Q and area of triangle ACR is 2 times area of triangle ABC: (( PQ)/(QR)).((AQ)/(QC)) is equal to (B) 1/10 (C) 2/5 (D) 3/5

Knowledge Check

  • The triangle is formed by joining the mid-points of the sides AB,BC and CA of triangle ABC and the area of triangle PQR is 6cm^2 , then the area of triangle ABC is :

    A
    `36cm^2`
    B
    `12cm^2`
    C
    `18cm^2`
    D
    `24cm^2`

  • In a triangle ABC, it is known that AB=AC. Suppose D is the mid-point of AC and BD=BC=2. Then the area of the triangle ABC is-

    A
    2
    B
    `2sqrt2`
    C
    `sqrt7`
    D
    `2sqrt7`

  • If veca , vecb, vecc are the position vectors of the vertices. A,B,C of a triangle ABC. Then the area of triangle ABC is

    A
    ` 1/2 |veca xx vecb +vecb xx vecc +vecc xx veca|`
    B
    `1/2|veca xx vecb|`
    C
    ` 1/2|vecb xx vecc|`
    D
    ` 1/2 |vecc xx veca|`

    • Similar Questions

    Explore conceptually related problems

    Let A,B,C be the vertices of a triangle ABC in which B is taken an origin of reference and position vectors of A and C bara and barc respectively. A line AR parallel to BC is drawn from A PR(P is mid point of AB) meets AC at Q and area of triangle ACR is 2 times area of triangle ABC. Positions vector of R in terms of bara and barc is z 1. 2. bara+3barc 3. bara+barc 4. bara+4barc Position vector of Q is (considering result of Q(7)). 1. (2bara+3barc)/5 2. (3bara+2barc)/5 3. (bara+2barc)/3 4. None of these (PQ/QR). (AQ/QC) is equal to 1. 1//4 2. 2//5 3. 3//5 1//6

    Consider a triangle OAB on the xy- plane in which O is taken as origin of reference and position vector of A and B are vec aandvec b respectively. A line AC parallel to OB is drawn a from A. D is the mid point of OA. Now a line DC meets AB at M. Area of DeltaABC is 2 times the area of DeltaOAB On the basis of above information, answer the following questions 1. Position vector of point C is 2. Position vector of point M is

    In the given figure, in triangle ABC, D is the mid-point cf AB and P is any point on BC. If CQ || PD meets AB in Q and area of triangle ABC = 30 cm2, then, area of triangle BPQ is

    Suppose P, Q and R are the mid-points of sides of a triangle of area 128 cm^2 . If a triangle ABC is drawn by joining the mid-points of sides of triangle PQR, then what is the area of triangle ABC?

    Let ABC be a triangle whose circumcenter is at P, if the positions vectors of A,B,C and P are veca,vecb,vecc and (veca + vecb+vecc)/4 respectively, then the positions vector of the orthocenter of this triangle, is:

    Home
    Profile