Question

Consider the following quadrilateral ABCD in which P, Q, R, S are the midpoints of the sides.

1. Find \(\overline{PQ} \,and\, \overline {SR}\) in terms of  \(\overline {AC}\)
2. Show that PQRS is a parallelogram.
3. If \(\bar a\) is any vector, prove that

\(\bar a = (\bar a.i)i + (\bar a. j)j+(\bar a.k)k\)

Answer 1

1. Using triangle law of addition, we get

2. From the above explanation we have,

3. Let \(\bar a\) = a₁ i + a₂ j + a₃ k