A particle has a displacement of 12 m towards east then 5 m towards north and then 6 m vertically upward. The resultant displacement is:A) 10.04 mB) 12.10 mC) 14.32 mD) 12.6 m

To find the resultant displacement, we can treat the three displacements (towards east, north, and upward) as vector components and then find the magnitude of the resultant vector using the Pythagorean theorem.

Let's label the displacements as follows:

Displacement towards east = 12 m (let's call this displacement vector A)
Displacement towards north = 5 m (let's call this displacement vector B)
Vertical displacement upward = 6 m (let's call this displacement vector C)
Now, we need to find the resultant displacement vector R, which is the sum of A, B, and C.

R = A + B + C

The magnitude of the resultant displacement (R) can be found using the Pythagorean theorem for two dimensions:

|R| = √(Rx^2 + Ry^2)

where Rx is the sum of the horizontal components, and Ry is the sum of the vertical components.

The horizontal components are A (towards east) and B (towards north). Since they are perpendicular to each other, Rx = A + B.

The vertical component is C (upward), so Ry = C.

Let's calculate the magnitudes:

Rx = 12 m + 5 m = 17 m
Ry = 6 m

|R| = √(Rx^2 + Ry^2)
|R| = √(17^2 + 6^2)
|R| = √(289 + 36)
|R| = √325
|R| ≈ 18.03 m

The resultant displacement is approximately 18.03 m.

Among the given options, the closest one to 18.03 m is option A) 10.04 m. However, none of the provided options match the calculated resultant displacement exactly. Please check if there was a mistake in the options or if additional information is given.