[" एक सरल रेखा "L" ,समांतर चतुर्भुज "ABCD" की भुजा "],[AB,AC,AD" को क्रमश: "B_(1),C_(1),D_(1)" पर काटती है। यदि "],[vec AB_(1)=lambda_(1)vec AB,vec AD_(1)=lambda_(2)vec AD" और "],[vec AC_(1)=lambda_(3)vec AC" हैं,तब "(1)/(lambda_(3))" बराबर है: "]

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 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 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 1/(lambda_3) .

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 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 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 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) .

Let B_(1),C_(1) and D_(1) are points on AB,AC and AD of the parallelogram ABCD , such that AB_(1)=k_(1)vec AC,AC_(1)=k_(2)vec AC and vec AD_(1)=k_(2)vec AD where k_(1),k_(2) and k_(3) are scalar.

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=