Find a vector in the direction of vector which has magnitude 8 units.
The given vector is a → = 5 i ^ − j ^ + 2 k ^ .
The magnitude of vector a → is,
| a → | = 5 2 + ( − 1 ) 2 + 2 2 = 30
Unit vector in direction of a → is,
a ^ = a → | a → | = 5 i ^ − j ^ + 2 k ^ 30 = 5 30 i ^ − 1 30 j ^ + 2 30 k ^
Vector equation in the direction of a → with magnitude 8 is,
8 a ^ = 8 ( 5 30 i ^ − 1 30 j ^ + 2 30 k ^ ) = 40 30 i ^ − 8 30 j ^ + 16 30 k ^
Thus, vector in the direction of a → with magnitude 8 is 40 30 i ^ − 8 30 j ^ + 16 30 k ^ .
The given vector is
The magnitude of vector
Unit vector in direction of
Vector equation in the direction of
Thus, vector in the direction of
which
has magnitude 8 units.