The position vectors of points P and R are (1, -3, 5) and (0, 3, 8) respectively. The distance vector between points Q and R is (2, 1, 2). The distance between points Q and R is the magnitude of this distance vector, which equals 5.

1. 1
Electrodynamics P.No.4
Given points (1,-3,5), (2,4,6),
and (0,3,8), find
(a) the position vectors of P and R,
(b) the distance vector ,
( ) the distance between Q and R.
QR
P Q
R
c
r
Solution
( )
(1, 3, 5)
3 5
(0, 3,8)
3 8
( )
(0, 3,8) (2, 4, 6)
( 2, 1, 2)
2 2
P
x y z
R
y z
QR R Q
x y z
a
P
R
b
R Q
= −
= − +
=
= +
= −
= −
= − −
= − − +
r
a a a
r
a a
r r r
a a a

2. 2
( )
from (b)
( 2, 1, 2)
4 1 4
9 3
QR
QR
c
= − −
 = + +
= =
r
r