Mathematics

Problem

Let the position vectors of two points in space be

\vec r_P = 1\,\hat i - 2\,\hat j + 3\,\hat k

and

\vec r_Q = 5\,\hat i + 1\,\hat j - 9\,\hat k

. a. (i) Write the displacement vector

\vec{PQ}

from

P

Q

. b. (ii) Compute the magnitude of

\vec{PQ}

. c. (iii) Obtain the unit vector along the line joining

P

and

Q

. d. (iv) State clearly which point the unit vector found in part (iii) points towards.