Question

A particle moves from position r1=3i+2j-6k to position r2= 14i+13j+9k under the action of force=4i+j+3k find work done

Answer 1

Work done is given by scalar (or dot) product of force and displacement vectors.

Here, displacement will be given as d = r' -r = [( 14i + 13j - 9k ) - ( 2i +j - 4k )] = ( 12i + 12j - 5k) m

Force , F = (4i +j +3k) N

so, the work done, W = F.d = (4i +j + 3k).(12i + 12j - 5k) = 4 × 12 + 1 × 12 + 3 × (-5) = 45 J

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Answer 2

ans is 100 joule

Explanation:

net displacement is r2-r1

(14-3)i +(13-2)j +(9-(-6))k

=11Ii+11j +15k

work done = force ×displacement

w=(4i+j+3k) × (11i+11j+15k)

=44+11+45

=100 joule