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Question

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

A
5(^i2^j+3^k) m/s
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B
5(4^i+2^j+3^k) m/s
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C
(0.6^i+0.8^j) m/s
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D
(6^i+8^j) m/s
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Solution

The correct option is D (6^i+8^j) m/s

Position vector of A rA=1^i2^j+3^k
Position vector of B rB=4^i+2^j+3^k

Displacement vector rBA:
rBA=rBrA=3^i+4^j

unit vector in the direction of bird's displacement is:-
^rBA=rBA|rBA|=3^i+4^j32+42=0.6^i+0.8^j

Speed of bird (v) = 10 m/s
v=v×^rBA=10×(0.6^i+0.8^j)
v=6^i+8^j m/s

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