Show that the vectors vector a = (1/7)(2i + 3j + 6k), vector b = (1/7)(3i - 6j + 2k), vector c = (1/7)(6i + 2j - 3k )

Question

Show that the vectors \(\vec a=\cfrac17(2\hat i+3\hat j+6\hat k),\)  \(\vec b=\cfrac17(3\hat i-6\hat j+2\hat k)\),  \(\vec c= \cfrac17(6\hat i+2\hat j-3\hat k)\) are mutually  perpendicular unit vectors.

Answer 1

Given Data:

\(\vec a=\cfrac17(2\hat i+3\hat j+6\hat k)\)

\(\vec b=\cfrac17(3\hat i-6\hat j+2\hat k)\)

\(\vec c= \cfrac17(6\hat i+2\hat j-3\hat k)\) 

\(\vec a.\vec b=0\)

Similarly,

Hence these vectors are mutually perpendicular.