सदिश ` hati +2hatj +3hatk ` की दिक्-कोज्यायें ज्ञात कीजिए|

Options

A. `(1)/(sqrt( 14)) , (1)/(sqrt( 14)), (3)/(sqrt( 13))`
B. `(1)/(sqrt( 14)) , (1)/(sqrt( 13)), (3)/(sqrt( 14))`
C. `(1)/(sqrt( 14)), (1)/(sqrt( 14)), (3)/(sqrt( 14))`
D. `(1)/(sqrt( 13)) , (1)/(sqrt( 14)), (3)/(sqrt( 14))`

Answer

C

Explanation

माना ` vecr =hati +2hatj +3hatk ` तब
` " "hatr =(vecr )/(|vecr |) =(hati +2hatj +3hatk )/( sqrt(1^(2) +2^(2) +3^(2) ) ) `
` rArr" " rArr hatr =(hati +2hatj +3hatk )/( sqrt (4) ) `
` rArr " " hatr =(1)/(sqrt( 14)) hati + (2)/(sqrt( 14) ) hatj +(3)/(sqrt( 14))hatk `
अतः सदिश ` vecr ` की दिक्-कोज्यायें ` (1)/(sqrt( 14)). (1)/(sqrt( 14)), (3)/(sqrt( 14))` है|