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महाराष्ट्र राज्य शिक्षण मंडळएचएससी विज्ञान (सामान्य) इयत्ता १२ वी

Find the values of c which satisfy |cu¯| = 3 where u¯=i^+2j^+3k^. - Mathematics and Statistics

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प्रश्न

Find the values of c which satisfy `|"c"overline"u"|` = 3 where `overline"u" = hat"i" + 2hat"j" + 3hat"k"`.

बेरीज

उत्तर

`|"c"overline"u"|` = 3

`overline"u"=hat"i"+2hat"j"+3hat"k"`

`vec"a"=xhat"i"+"y"hat"j"+"z"hat"k"`

`|overline"a"|=sqrt(x^2+"y"^2+"z"^2)`

⇒ `|vec"u"|=sqrt((1)^2+(2)^2+(3)^2)`

= `sqrt(14)`

= c`|vec"u"|` = 3

c`sqrt14` = 3

∴ c = `3/sqrt(14)`

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