Question

Find the position vector of the mid point of the vector joining the points P (2, 3, 4) and Q (4, 1, – 2).

Answer 1

The given points are P( 2,3,4 ) and Q( 4,1,−2 ).

Position vector of P is,

OP → =( 2−0 ) i ^ +( 3−0 ) j ^ +( 4−0 ) k ^ =2 i ^ +3 j ^ +4 k ^

Position vector of Q is,

OQ → =( 4−0 ) i ^ +( 1−0 ) j ^ +( −2−0 ) k ^ =4 i ^ + j ^ −2 k ^

Let R be the midpoint of line PQ.

Position vector of mid point R is,

OR → = OQ → + OP → 1+1 = ( 4 i ^ + j ^ −2 k ^ )+( 2 i ^ +3 j ^ +4 k ^ ) 2 = 6 i ^ +4 j ^ +2 k ^ 2 =3 i ^ +2 j ^ + k ^

Thus, the position vector of midpoint of line PQ is 3 i ^ +2 j ^ + k ^ .