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A bird moves from point (1, -2, 3) to (4...

A bird moves from point `(1, -2, 3)` to `(4, 2, 3)`. If the speed of the bird id `10 m//s`, then the velocity of the bird is :-

A

`5 (hati-2hatj+3hatk)`

B

`5 (4hati+2hatj+3hatk)`

C

`0.6 hat(i)+0.8 hat(j)`

D

`6hat(i)+8hat(j)`

Text Solution

Verified by Experts

The correct Answer is:
D
`vec(v)=((4-1)hat(i)+(2+2)hat(j)+(3-3)hat(k))/sqrt(3^(2)+4^(2)+0^(2))=(3hati+4hatj)/5`
`vec(v)=|vec(v)|hat(v)=10((3hat(i)+4hatj)/5)=6hat(i)+8hat(j)`
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Knowledge Check

  • A bird moves from point (1 m, -2 m, 3 m) to (4 m, 2 m, 3 m) . If the speed of the bird is 10 m//s , then the velocity vector of the bird in m//s is:

    A
    `5(hat(i)-2hat(j)+3hat(k))`
    B
    `5(4hat(i)+2hat(j)+3hat(k))`
    C
    `0.6 hat(i)+0.8 hat(j)`
    D
    `6hat(i)+8hat(j)`

  • A bird flies to and fro between two cars which moves with velocities v_1 = 20 m//s and v_2 = 30 m//s . If the speed of the bird is v_3 = 10 m//s and the initial distance of separation between them is d = 2 km , find the total distance covered by the bird till the cars meet.

    A
    2000 m
    B
    1000 m
    C
    400 m
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  • A bird flies from (-3m, 4m, -3 m) to (7m, -2m, -3m) in the xyz-coordinates. The bird's displacement vector is given by

    A
    `(4hati + 2hatj - 6hatk)`
    B
    `(10 hati - 6hatj)`
    C
    `(4 hati - 2hatj)`
    D
    `(10 hati + 6 hatj - 6hatk)`

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