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If ` hat a\ a n d\ hat b` are unit vectors inclined at an angle `theta` then prove that `costheta/2=1/2| hat a+ hat b|` `tantheta/2=(| hat a- hat b|)/(| hat a+ hat b|)`

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`|hat(a)+hat(b)|^(2)=(hat(a)+hat(b)).(hat(a)+hat(b))=hat(a).hat(a)+hat(a).hat(b)+hat(b).hat(a)+hat(b).hat(b)`
`=|hat(a)|^(2)+2(hat(a).hat(b))+|hat(b)|^(2)=1+2|hat(a)||hat(b)| cos theta+1`
`=2(1+cos theta)=2xx2 "cos"^(2) theta/2=4 "cos"^(2) theta/2`.
`:. "cos" theta/2=1/2 |hat(a)+hat(b)|`.
Similarly, we have `|hat(a)-hat(b)|^(2)=4 "sin"^(2) theta/2`.
`:. "sin" theta/2=1/2 |hat(a)-hat(b)|`.
Hence, `"tan" theta/2=(|hat(a)-hat(b)|)/(|hat(a)+hat(b)|)`
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RS AGGARWAL-SCALAR, OR DOT, PRODUCT OF VECTORS-Exercise 23
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  12. If vec(AB)=(3hat(i)-hat(j)+2hat(k)) and the coordinates of A are (0, -...

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  16. Three vertices of a triangle are A(0, -1, -2), B(3, 1, 4) and C(5, 7, ...

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