At a given instant of time two particles are having the position vectors $4 \hat i+4 \hat j+57 \hat k$ metres and $2 \hat i+2 \hat j+5 \hat k$ respectively. If the velocity of the first particle be $0.4 \hat i ms^{-1},$ the velocity of second particle in meter per second if they collide after 10 sec is :

Question

\[\begin {array} {1 1} (a)\;6 \bigg(\hat i- \hat j+\frac{1}{3} \hat k \bigg) & \quad (b)\;0.6 \bigg(\hat i-\hat j+\frac{1}{3} \hat k\bigg) \\ (c)\;6 \bigg(\hat i+\hat j+\frac{1}{3} \hat k\bigg) & \quad (d)\;0.6 \bigg(\hat i+\hat j-\frac{1}{3} \hat k\bigg) \end {array}\]