If vector a = i + j, vector b = j + k and vector c = k + i, write unit vectors parallel to vector a + vector b - 2 vector c.

Question

If \(\vec a=\hat i + \hat j,\) \(\vec b=\hat j+\hat k\)  and \(\vec c=\hat k+\hat i,\)  write unit vectors parallel to  \(\vec a+\vec b-2\vec c.\)

Answer 1

Given that

The unit vector of any vector  \(\vec a=a_1\hat i+a_2\hat j+a_2\hat k\) can be written as 

Let \(\vec d=\vec a+\vec b-2\vec c\)

Then,

Both  \(\vec d\) and \(-\hat d,\) therefore the answer is