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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)` .

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