Question

A force f = 3i + cj + 2k acting on a particle causes a displacement: x = - 4i + j + 3k in its own direction. If the work done is 6 joule then the value of ‘c' is?

Answer 1

Hey!

since work= force * displacement of body

6= (3i+cj+2k)*(-4i+j+3k)
6=(3*-4)i*i+(c*1)j*j+(2*3)k*k
..
(since i*i=1....)
6= -12+c+6

c=12
Here is yr ans!

Answer 2

Answer:

c = 12

Explanation:

Given that,

Force acting on the particle, F = 3i+cj+2k

Displacement of the particle, d = -4i+j+3k

Work done by the particle, W = 6 J

We know that the dot product of force and the displacement gives the amount of work done by the object. Mathematically,

$W=F.d$

$6=(3i+cj+2k).(-4i+j+3k)$

We know that,

i.i = j.j = k.k = 1

$6=-12+c+6$

c = 12

So, the value of c is 12. Hence, this is the required solution.