3 particles start from origin with velocity $u_{1}, u_{2} and u_{3}$ $u_1,u_2 and u_3$ .They are moving with constant velocities.Find the relation between $u_{1}, u_{2} and u_{3}$ $u_1,u_2 and u_3$ so that all 3 particles lie on the same plane?

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Answer 1 · 2018-03-19T10:31:32

$({\to u}_{1} - {\to u}_{2}) \times ({\to u}_{1} - {\to u}_{3}) \neq \to 0$ $(vec u_1-vec u_2) xx (vec u_1- vec u_3) ne vec 0$

The path for the particles is given by

$p_{i} = p_{0} + t {\to u}_{i}$ $p_i = p_0 + t vec u_i$

with $p_{0} = (0, 0, 0)$ $p_0 = (0,0,0)$

The condition for non-alignment is

$(p_{1} - p_{2}) \times (p_{1} - p_{3}) \neq \to 0$ $(p_1-p_2) xx (p_1-p_3) ne vec 0$ or

$(t {\to u}_{1} - t {\to u}_{2}) \times (t {\to u}_{1} - t {\to u}_{3}) \neq \to 0$ $(t vec u_1-t vec u_2) xx (t vec u_1- t vec u_3) ne vec 0$

or

$({\to u}_{1} - {\to u}_{2}) \times ({\to u}_{1} - {\to u}_{3}) \neq \to 0$ $(vec u_1-vec u_2) xx (vec u_1- vec u_3) ne vec 0$

3 particles start from origin with velocity u1,u2andu3u_1,u_2 and u_3.They are moving with constant velocities.Find the relation between u1,u2andu3u_1,u_2 and u_3 so that all 3 particles lie on the same plane?