Write two different vectors having same direction.
For same directions, vectors should have same direction cosines.
Assume, the two different vectors are a → = 1 i ^ + 1 j ^ + 1 k ^ and b → = 3 i ^ + 3 j ^ + 3 k ^ .
Magnitude of a → is,
| a → | = 1 2 + 1 2 + 1 2 = 3
Direction cosines of a → are ( x | a → | , y | a → | , z | a → | ) .
Here, x = 1 , y = 1 and z = 1 .
Substitute all values for direction cosines, we get,
( 1 3 , 1 3 , 1 3 )
Magnitude of b → is,
| b → | = 3 2 + 3 2 + 3 2 = 3 1 + 1 + 1 = 3 3
Direction cosines of b → are ( x | b → | , y | b → | , z | b → | ) .
Here, x = 3 , y = 3 and z = 3 .
Substitute all values for direction cosines, we get,
( 1 3 , 1 3 , 1 3 )
Thus, the two different vectors having same direction cosines are a → = 1 i ^ + 1 j ^ + 1 k ^ and b → = 3 i ^ + 3 j ^ + 3 k ^ .
For same directions, vectors should have same direction cosines.
Assume, the two different vectors are
Magnitude of
Direction cosines of
Here,
Substitute all values for direction cosines, we get,
Magnitude of
Direction cosines of
Here,
Substitute all values for direction cosines, we get,
Thus, the two different vectors having same direction cosines are
