A body moves 6 𝑚 north, 8 𝑚 east and10m vertically upwards, what is itsresultant displacement from initialposition

The displacement of the body can be calculated using the Pythagorean theorem in three dimensions. The Pythagorean theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. This can be written as:

a² + b² + c² = d²

where:

• a, b and c are the lengths of the sides of the triangle (in this case, the distances the body moves in the north, east and upwards directions), and
• d is the length of the hypotenuse (in this case, the resultant displacement of the body from its initial position).

Given that the body moves 6 m north, 8 m east and 10 m vertically upwards, we can substitute these values into the equation to find the resultant displacement:

(6 m)² + (8 m)² + (10 m)² = d²

36 m² + 64 m² + 100 m² = d²

200 m² = d²

Taking the square root of both sides of the equation gives the length of d:

d = √200 m

d = 14.14 m

So, the resultant displacement of the body from its initial position is approximately 14.14 m.