Find the angle between the vectors vector a and vector b, where: vector a = 2i - 3j + k and vector b = i + j - 2k

Question

Find the angle between the vectors  \(\vec a\) and  \(\vec b\), where:

\(\vec a=2\hat i-3\hat j+\hat k\)  and  \(\vec b = \hat i+\hat j - 2\hat k\)

Answer 1

 Using formula  \(\vec a.\vec b=|\vec a|\times|\vec b|\times cos\theta\) 

 \(\vec a=2\hat i-3\hat j+\hat k\)  

  \(\vec b = \hat i+\hat j - 2\hat k\)

Therefore angle between  \(\vec a\) and  \(\vec b\) is  \(cos^{-1}(-\cfrac{3}{\sqrt{84}})\).