The equation of motion of a missile is x = 3t, y = -4t, z = t where time 't' is in seconds and the distance is measured in kilometres.

At what distance will the rocket be from the point (0, 0, 0) in 5 seconds?

$\sqrt{650}$ kms

The correct answer is Option (3) → $\sqrt{650}$ kms

let coordinates after 5 sec be

$P(x, y, z)$

at $t=5$

$x=3×5=15$

$y=-4×5=-20$

$z=5$

so $P(15,-20,5)$

so $O(0,0,0)$

$OP=\sqrt{15^2+20^2+5^2}$

$=\sqrt{225+400+25}$

$=\sqrt{650}$ kms