Two particles are located at it →r₁ = 3ˆi + 7ˆj and →r₂ = -2ˆi + 3ˆj respectively. Find both the magnitude of the vector →r₂ - →r₁ and its orientation with respect to the x-axis. [Ans: 6.4, 219°]


Given:

→r₁ = 3ˆi + 7ˆj 
→r₂ = -2ˆi + 3ˆj


To Find:

Magnitude of the Position Vector = |→r| = 
|→r₂ - →r₁| = ?
Orientation with respect to X-asis = Ө = ?


Solution: 

As we are given 

→r = →r₂ - →r₁ 

→r = (-2ˆi + 3ˆj) - (3ˆi + 7ˆj)

→r = -5ˆi - 4 ˆj

Here x-component = -5 and the y-component = -4 . So, to find its magnitude |→r| we have

|→r| = √x2+y2

by putting values 

r = √(-5)2+(-4)2

r = √25+16

r = √41

r = 6.4    --------Ans (1)

Thus the magnitude of the vector →r₂ - →r₁ 6.4

For direction (orientation w.r.t. X-axis) we have the formula

tan Ө = yx

or

Ө =  tan⁻¹ yx

by putting value of x and y


Ө =  tan⁻¹ -4-5

Ө =  tan⁻¹ (0.8)

Ө =  39⁰

As x-component = -5 and y-component = -4 (both are negative) therefore it lies in the 3rd quadrant. so we will 180⁰ to the angle for the 3rd quadrant. i.e.

Ө =  180⁰  + 39⁰

Ө =  219⁰  --------Ans (2)
 
Thus the Orientation of the vector →r₂ - →r₁ with respect to x-asis  is 219⁰ 


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Numerical Problem 2.4
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List of 11th Physics Numerical Problems of Chapter - 2
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