If vector a = i + 2j, vector b = j +2k, write a unit vector along the vector 3 vector a- 2 vector b.

Question

If vector \(\vec a=i+2\vec j,\)  \(\vec b=\hat j+2\vec k,\)  write a unit vector along the vector \(3\vec a-2\vec b\).

Answer 1

Given that

The unit vector of any vector \(\vec a=a_1\hat i+a_2\hat j+a_3\hat k\) can be written as

Let  \(\vec d=3\vec a-2\vec b\) 

Then,

The unit vector in direction of \(\vec d\) is  \(\hat d\).th widget