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Shane Macguire Grade: upto college level
        A particle moves on a given straight line with a constant speed v. At a certain time it is at a point P on its straight line path. O is a fixed point. Show that (OP) ⃗×v ⃗ is independent of the position P.
3 years ago

Answers : (1)

Deepak Patra
askIITians Faculty
474 Points
										 Sol. The particle moves on the straight line PP’ at speed v.
From the figure,

(OP) ⃗ v =  (OP)v sin θ n ̂ = v(OP) sin θ n ̂ = v(OQ) n ̂
It can be seen from the figure, OQ = OP sin θ = OP’ sin θ’
So, whatever may be the position of the particle, the magnitude and

direction of (OP) ⃗ v ⃗  remain constant.
∴ (OP) ⃗ x  v ⃗  is independent of the position P.

3 years ago
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