Question

a force of 3i -2j+4k displace an object from a point ( 1, 1, 1) to another (2, 0, 3) the work done by force is
A. 10
B. 12
C. 13
D. 29
E. non of these

Answer 1

F = 3i -2j+4k
Dispcament vector, S = (2-1)i+(0-1)j+(3-1)k = i - j + 2k

Work Done ,
W = F . S
= ( 3i -2j+4k ) . (i - j + 2k)
= 3 + 2 + 8 = 13 Joules

Answer 2

Answer:

The work done by the force is 13 J.

(C) is correct.

Explanation:

Given that,

Force $F = 3i-2j+4k$

Initial point =(1,1,1)

Final point =(2,0,3)

The displacement of the object is

Displacement = final point -initial point

$D=(2-1)i+(0-1)j+(3-1)k$

$D=1i-1j+2k$

The work done is the dot product of the force and displacement.

The work done by the force is

$W = F\cdot D$

$W=(3i-2j+4k)\cdot (1i-1j+2k)$

$W=3+2+8=13\ J$

Hence, The work done by the force is 13 J.