An object is displaced from position vector r-1- 2-3- m to r-2- 4-6- m under a force F- 3x2-2y- N- Find the work done by this force-

An object has a displacement from position vector $_{1} = (2^i + 3^j) m$
to $_{2} = (4^i + 6^j) m$ under a force $\to F = (3 x^{2}^i + 2 y^j) N,$ then work done by the force is:

Q. An object is displaced from position vector

{\to r}_{1} = (2^i + 3^j) m

{\to r}_{2} = (4^i + 6^j) m

under the action of a force

\to F = (3 x^{2}^i + 2 y^j) N

. Find the work done by this force.

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An object is displaced from position vector →r1=(2^i+3^j)m to→r2=(4^i+6^j) m under a force →F=(3x2^i+2y^j)N. Find the work done by this force.

The correct option is A 83JW=∫→r2→r1→F⋅→dr=∫→r2→r1(3x2^i+2y^j)⋅(dx^i+dy^j+dz^k)=∫→r2→r1(3x2dx+2ydy)=[x3+y2](4,6)(2,3)=83J

An object is displaced from position vector ${\to r}_{1} = (2^i + 3^j) m$ to ${\to r}_{2} = (4^i + 6^j)$ m under a force $\to F = (3 x^{2}^i + 2 y^j) N .$ Find the work done by this force.

The correct option is A $83 J$
$W = \int_{{\to r}_{1}}^{{\to r}_{2}} \to F \cdot \to d r$

$= \int_{{\to r}_{1}}^{{\to r}_{2}} (3 x^{2}^i + 2 y^j) \cdot (d x^i + d y^j + d z^k)$

$= \int_{{\to r}_{1}}^{{\to r}_{2}} (3 x^{2} d x + 2 y d y) = {[x^{3} + y^{2}]}_{(2, 3)}^{3}$

$= 83 J$