Find the angle between the vectors i−j and j−k - Mathematics

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Find the angle between the vectors `hati-hatj and hatj-hatk`

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Solution

`Let veca = hati − hatj; vecb = hatj− hatk`

`veca . vecb=(hat i-hat j).(hat j-hat k)=` 1 x 0 +(-1) x  1 + 0 x (-1)=-1

`|veca|=sqrt(1^2+(-1)^2+0^2)=sqrt2`

`|vecb|=sqrt(0^2+1^2+(_1)^2)=sqrt2`

We know that `veca.vecb=|veca||vecb|cos theta`

Thus,`costheta=(veca.vecb)/(|veca||vecb|)=-1/(sqrt2 xx sqrt2)=-1/2`

`=> costheta=cos 120^@`

`=> theta= 120^@`

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2014-2015 (March) Panchkula Set 1

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