Question

A force \[\vec F\] = 3\[\hat i\] + c\[\hat j\] + 2\[\hat k\] acting on a particle displaces it. The displacement is given by \[\vec s\] = 4\[\hat i\] + 2\[\hat j\] + 3\[\hat k\] in its own direction. If the work done is 6 J, then value of 'c' is ______.

Options

• 0

• 1

• -6

• 12

Answer 1

A force \[\vec F\] = 3\[\hat i\] + c\[\hat j\] + 2\[\hat k\] acting on a particle displaces it. The displacement is given by \[\vec s\] = 4\[\hat i\] + 2\[\hat j\] + 3\[\hat k\] in its own direction. If the work done is 6 J, then value of 'c' is -6.

Explanation:

W = \[\vec F\] . \[\vec s\]

\[\therefore\] 6 = \[\begin{pmatrix} 3\hat{\mathrm{i}}+\mathrm{c}\hat{\mathrm{j}}+2\hat{\mathrm{k}} \end{pmatrix} \begin{pmatrix} 4\hat{\mathrm{i}}+2\hat{\mathrm{j}}+3\hat{\mathrm{k}} \end{pmatrix}\]

\[\therefore\] 6 = 12 + 2c + 6

6 = 18 +12c

2c = -12

c = -6