परिमाण ` 5sqrt2` की एक सदिश ` veca ` ज्ञात कीजिए जो X अक्ष के साथ ` (pi)/(4),Y-` अक्ष के साथ ` (pi)/(2) ` और Z अक्ष के साथ न्यूनकोण ` theta ` बनाती है

दिया गया है की ` -alpha =(pi)/(4) ,beta =(pi)/(2) ,gamma =theta `
` therefore " "l=cos ""(pi)/(4) =(1)/(sqrt(2))`
` " "mcos ""(pi)/(2) =0 `
` " "n=cos theta `
हम जानते है की
`" "l^(2) +m^(2) +n^(2) =1 `
`rArr" "((1)/(sqrt(2))) ^(2) + 0+ n^(2) =1`
` rArr " "(1)/(2) +n^(2) =1`
`rArr " "n^(2) =1 -(1)/(2)`
` rArr " "n^(2) =(1)/(2) `
` cos ^(2) theta =(1)/(2)`
` rArr " "cos theta =(1)/(sqrt(2))" " [because theta ` न्यूनकोण है]
`rArr " "theta =(pi)/(4)`
` therefore " "n=cos theta =(1)/(sqrt(2) ) `
अतः सदिश की दिक्-कोज्याएँ` (1)/(sqrt( 2) ),0 (1)/(sqrt( 2) ) ` है|
` therefore` सदिश ` vec a=|vec a| (lhati +mhatj +nhatk ) `
` " " = 5sqrt(2) ((1)/(2) hati +0hatj +(1)/(sqrt(2))hatk ) `
` " "= (5sqrt2)/(sqrt2)(hati +hatk ) `
` " " = 5 (hati +hatk ) `