Three particles start from the origin at the same time, one with a velocity `v_(1)` along the x-axis, second along the negative y-axis with a velocity `v_(2)` and third particle moves along the line x = y. The velocity of third particle, so that three may always lie on the same line is:

Options

A. `( v_1v_2)/( v_1+v_2) `
B. ` (sqrt(2)v_1v_2)/(v_1+v_2)`
C. ` (sqrt( 3)v_1v_2)/(v_1+v_2) `
D. zero

Answer

B

Explanation

After time t, the particles reach A ,B ,& C
` (##VMC_PHY_XI_WOR_BOK_01_C02_E03_005_S01.png" width="80%">
` " " OA =V_1t`
`" " OB =v_2t `
` " "OC =V_3t`
` " "` Coordinates : A ` ( v_1t.0) ,B( 0,v_2t) , C( (v_3)/(sqrt( 2)) t,(V_3)/(sqrt((2))t) `
Line AB :` (x)/( v_1t) +(y)/(v_2t) =1 " " ` C should lie on AB,
` (V_3)/(V_1sqrt2)+(V_3)/(v_2sqrt(2)=1 " "," " 1//v_3=((v_1+v_2)/(sqrt 2v_1v_2) " "," " v_3 =(sqrt( 2)v_1v_2)/(v_1+v_2) `