Two particles A and B are placed in gravity free space at `(0, 0, 0) m and (30, 0, 0) m` respectively. Particle A is projected with a velocity `(5hat i + 10 hat j + 5 hat k) ms^-1,` while particle B is projected with a velocity `(10 hat i + 5 hat j + 5 hat k) ms^-1` simultaneously. Then,

Options

A. they will collide at `(10, 20, 10) m`
B. they will collide at `(10, 10, 10) m`
C. they will never collide
D. they will collide at 2 s

Answer

C

Explanation

For collision,
`r_A=r_b` (at same instant)
`:. (r_i+v_t)_A=(r_i+v_t)_B`
`rArr (5 hati+10 hatj+5 hatk)t=30 hati+(10 hati+5 hatj+5 hatk)t`
Equating the coefficients of x
`5t=30+10t`
`rArr t=-ve`
So, they will never collide.