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Question

What are the initial position vector ri and final position vector rf, both in unit-vector notation? What is the x component of displacement Δr?

(i)

Position vector ri

(x)

5^i3^j1^k

(ii)

Postion vector rf

(y)

2^i4^j+1^k

(iii)

x-component of displacement Δr

(z)

7^i+1^j2^k


A

(i) - (x); (ii) - (z); (iii) - (y)

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B

(i) - (z); (ii) - (x); (iii) - (y)

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C

(i) - (z); (ii) - (y); (iii) - (x)

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D

(i) - (x); (ii) - (y); (iii) - (z)

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Solution

The correct option is B

(i) - (z); (ii) - (x); (iii) - (y)



By looking at the picture, I can say to reach i from 0, I have walked 7m on the x-axis, 1m on the y-axis and 2m on the -ve z-axis.
So my ri=7^i+1^j2^k, similarly rf=5^i3^j1^k. Now displacement vector is rfri=Δr
(5^i3^j1^k)(7^i+1^j2^k)
r=2^i4^j+1^k
This means to reach point 'f' from i we have to walk 2m in the -ve x-axis then 4m on -ve y-axis and then 1m on +ve axis so x-component or the displacement along the positive direction of x-axis is -2m.


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