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At t=0, a particle at (1,0,0) moves towa...

At `t=0`, a particle at `(1,0,0)` moves towards point `(4,4,12)` with a constant velocity of magnitude `65m//s`. The position of the particle is measured in metres and time in sec. Assuming constant velocity, the position of the particle at `t=2 sec` is `:`

A

`(13hat(i)-120hat(j)+40hat(k))m`

B

`(40hat(i)+31hat(j)-120hat(k))m`

C

`(13hat(i)-40hat(j)+12hat(k))m`

D

`(31hat(i)+40hat(j)+120hat(k))m`

Text Solution

Verified by Experts

The correct Answer is:
D
Unit vector in direction of `(1,0,0)` to `(4,4,12)` is `((4-1)hat(i)+(4,0)hat(j)+(12-0)hat(k))/(13)`
Hence position of particle at `t=2 sec` is `:`
`vec(r)_(f)=vec(r)_(i)+vec(v)xx2=31hat(i)+40hat(j)+120hat(k)`
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