1.

एक सदिश `vecr` का x-अक्ष के झुकाव `45^(@)` और y - अक्ष से झुकाव `60^(@)` है यदि`|vecr|=8 ,` तो `vecr` ज्ञात कीजिए ।

Answer» यहाँ ` alpha = 45^(@) , beta = 60^(@)`
हम जानते है कि `l = cos alpha , m= cos 60^(@)`
`implies l= cos 45^(@), m= cos 60^(@)`
`implies l=(1)/(sqrt(2)), m=(1)/(2)`
और `l^(2)+m^(2)+n^(2)=1`
`implies (1)/(2)+(1)/(4)+n^(2)=1`
`implies(1)/(2)+(1)/(4)+n^(2)=1`
`implies n^(2)=(1)/(4)`
`implies n=+- (1)/(2)`
`therefore hatr = l hati +m hatj+nhatk =(1)/(sqrt(2))hati+(1)/(2)hatj +- (1)/(2) hatk`
प्रश्नानुसार `|vecr|=8`
` therefore vecr = 8 hatr`
`=8((1)/(sqrt(2))hati + (1)/(2) hatj +- (1)/(2) hatk )=4 ( sqrt(2) hati + hatj + hatk)`


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