Mathematics

Problem

With respect to origin

O

, the position vectors of the vertices of a triangle are

\mathbf{A}=2\,\mathbf{\hat{i}}+3\,\mathbf{\hat{j}}

\mathbf{B}=-4\,\mathbf{\hat{i}}+5\,\mathbf{\hat{j}}

, and

\mathbf{C}=6\,\mathbf{\hat{i}}-1\,\mathbf{\hat{j}}

. a. (i) Obtain the vector representing the median drawn from vertex

A

to side

BC

. b. (ii) Determine the unit vector

\mathbf{\hat{m}}

along this median. c. (iii) Find the length of the median. d. (iv) A force of

10\,\text{N}

acts along the direction of the median found in part (ii). Express this force vector in component form.