A bird starts from `(1,0,0)` in the direction `(2hati+3hatj-6hatk)` with a speed `21 m//s` for `5` sec,then along the direction `(3hati+4hatj+5hatk)`with a speed `5sqrt2m//s` for `5` sec. Find the final displacement of the bird so that it reaches the origin?

Options

A. `30hati+45hatj-45hatk`
B. `-45hati-65hatj+65hatk`
C. `-46hati-65hatj+65hatk`
D. `46hati-65hatj-65hatk`

Answer

C

Explanation

`vec(r_(i))=hat(j)`
`vec(d_(1))=21xx5[(2hat(i)+3hat(j)-6hat(k))/(7)]=30hat(i)+45hat(j)-90hat(k)`
`vec(d_(2))=5sqrt(2)xx5[[3hati+45hatj-90hatk]]/(5sqrt(2))`
`=15hat(i)+20hat(j)+25hat(k)`
`d_(Net)=45hati+65hatj-65hatk`
`rArrvec(r_(f))=46hat(i)+65hat(j)-65hat(k)`
For zero displacement
`vec(d_(f))=-(r_(f))=-(46hat(i)+65hat(j)-65hat(k))`
`=-46hat(i)-65hat(j)+65hat(k)`