दो सदिश ` vec a = 2hati + hatj + 3hatk ` तथा ` vec b = 3hati - 2hatj + hatk ` है | सिद्ध कीजिए की इनके बिच का कोण `60^(@)` है |

Explanation

` vec a . vecb = (2hati + hatj + 3hatk). (3hati - 2hatj + hatk)`
`= 6(hati.hati) -2 (hatj . hatj) +3(hatk . hatk )`
` = 6 - 2 + 3 = 7`
`|veca| = |2hati + hatj + 3hatk = sqrt((2)^(2) + (1)^(2) + (3)^(2)] = sqrt(14)`
तथा ` |vec b| = |3hati - 2 hatj + hatk | = sqrt([(3)^(2) +(-2 )^(2)(1)^(2)]) = sqrt(14)`
अब , `cos theta = (veca.vecb)/(|veca|. |vecb|) = (7)/(sqrt(14) xx sqrt(14)) = (7)/(14) = (1)/(2)`
` rArr theta = cos^(-1) ((1)/(2)) rArr theta = 60^(2)` .