Question

Find the unit vector in the direction of vector , where P and Q are the points (1, 2, 3) and (4, 5, 6), respectively.

Answer 1

The initial point of the vector is P( 1,2,3 )and terminal point is Q( 4,5,6 ).

Formula for vector equation when initial and terminal points are given is,

PQ → =( x 2 − x 1 ) i ^ +( y 2 − y 1 ) j ^ +( z 2 − z 1 ) k ^

Here, x 1 =1, x 2 =4, y 1 =2, y 2 =5, z 1 =3 and z 2 =6.

Substitute all values in the above formula we get,

PQ → =( 4−1 ) i ^ +( 5−2 ) j ^ +( 6−3 ) z ^ =3 i ^ +3 j ^ +3 z ^

The magnitude of vector PQ → .

PQ → = 3 2 + 3 2 + 3 2 = 27 =3 3

Unit vector in direction of PQ → is,

PQ → | PQ → | = 3 i ^ +3 j ^ +3 z ^ 3 3 = 1 3 i ^ + 1 3 j ^ + 1 3 k ^

Thus, the unit vector in direction of PQ → is 1 3 i ^ + 1 3 j ^ + 1 3 k ^ .