Home
Class 12
MATHS
A straight line L cuts the lines A B ,A ...

A straight line `L` cuts the lines `A B ,A Ca n dA D` of a parallelogram `A B C D` at points `B_1, C_1a n dD_1,` respectively. If `( vec A B)_1,lambda_1 vec A B ,( vec A D)_1=lambda_2 vec A Da n d( vec A C)_1=lambda_3 vec A C ,` then prove that `1/(lambda_3)=1/(lambda_1)+1/(lambda_2)` .

A

`(1)/(lambda_1)+(1)/(lambda_2)`

B

`(1)/(lambda_1)-(1)/(lambda_2)`

C

`-(lambda_1)+(lambda_2)`

D

`(lambda_1)+(lambda_2)`

Text Solution

Verified by Experts

The correct Answer is:
(a)
Promotional Banner

Topper's Solved these Questions

  • THREE DIMENSIONAL COORDINATE SYSTEM

    ARIHANT MATHS ENGLISH|Exercise JEE Type Solved Examples : Matching Type Questions|4 Videos

  • THREE DIMENSIONAL COORDINATE SYSTEM

    ARIHANT MATHS ENGLISH|Exercise Exercise For Session 1|12 Videos

  • THEORY OF EQUATIONS

    ARIHANT MATHS ENGLISH|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|35 Videos

  • TRIGONOMETRIC EQUATIONS AND INEQUATIONS

    ARIHANT MATHS ENGLISH|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|12 Videos

Similar Questions

Explore conceptually related problems

A straight line L cuts the sides AB, AC, AD of a parallelogram ABCD at B_(1), C_(1), d_(1) respectively. If vec(AB_(1))=lambda_(1)vec(AB), vec(AD_(1))=lambda_(2)vec(AD) and vec(AC_(1))=lambda_(3)vec(AC),

A straight line L cuts the sides AB, AC, AD of a parallelogram ABCD at B_(1), C_(1), d_(1) respectively. If vec(AB_(1))=lambda_(1)vec(AB), vec(AD_(1))=lambda_(2)vec(AD) and vec(AC_(1))=lambda_(3)vec(AC), then (1)/(lambda_(3)) equal to

A B C D parallelogram, and A_1a n dB_1 are the midpoints of sides B Ca n dC D , respectivley . If vec A A_1+ vec A B_1=lambda vec A C ,t h e nlambda is equal to a. 1/2 b. 1 c. 3/2 d. 2 e. 2/3

A B C D is a parallelogram. If La n dM are the mid-points of B Ca n dD C respectively, then express vec A La n d vec A M in terms of vec A Ba n d vec A D . Also, prove that vec A L+ vec A M=3/2 vec A Cdot

A B C D isa parallelogram with A C\ a n d\ B D as diagonals. Then, vec A C- vec B D= 4 vec A B b. 3 vec A B c. 2 vec A B d. vec A B

Find | vec a- vec b|,\ if:| vec a|=3,\ | vec b|=4\ a n d\ vec adot vec b=1

Write the condition for the lines vec r= vec a_1+lambda vec b_1 a n d\ vec r= vec a_2+mu vec b_2dot\ to be intersecting.

If D,E and F are the mid-points of the sides BC, CA and AB respectively of a triangle ABC and lambda is scalar, such that vec(AD) + 2/3vec(BE)+1/3vec(CF)=lambdavec(AC) , then lambda is equal to

If D is the mid point of side BC of a triangle ABC such that vec A B+ vec A C=lambda\ vec A D , write the value of lambdadot

If [ 2 vec (a) - 3 vec(b) vec( c ) vec(d)] =lambda [vec(a) vec(c ) vec(d) ] + mu [ vec(b) vec( c ) vec( d) ] , then 2 lambda + 3 mu=