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Question

Write two different vectors having same direction.

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Solution

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 ^ .


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