3 particles start from origin with velocity #u_1,u_2 and u_3#.They are moving with constant velocities.Find the relation between #u_1,u_2 and u_3# so that all 3 particles lie on the same plane?

Question

1049 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-03-19T10:31:32

#(vec u_1-vec u_2) xx (vec u_1- vec u_3) ne vec 0#

The path for the particles is given by

#p_i = p_0 + t vec u_i#

with #p_0 = (0,0,0)#

The condition for non-alignment is

#(p_1-p_2) xx (p_1-p_3) ne vec 0# or

#(t vec u_1-t vec u_2) xx (t vec u_1- t vec u_3) ne vec 0#

or

#(vec u_1-vec u_2) xx (vec u_1- vec u_3) ne vec 0#