Mass is located at point and mass is located at point in a Cartesian coordinate system

PHYSICS · Subjective · A Level · Physics · Fields and their consequences · Fields and their consequences

Problem

Mass

m_1 = 2.0\,\text{kg}

is located at point

A(0,\,0,\,0)

and mass

m_2 = 3.0\,\text{kg}

is located at point

B(0.30\,\text{m},\,0.40\,\text{m},\,0.00\,\text{m})

in a Cartesian coordinate system. (i) Determine the position vector

\mathbf r_{12}

from

m_1

m_2

and its magnitude

r

. (ii) Hence calculate the gravitational force vector

\mathbf F_{12}

acting on

m_1

due to

m_2

in unit-vector notation. (iii) Write the gravitational force vector acting on

m_2

due to

m_1

and verify that the two forces are equal in magnitude and opposite in direction.