1.

Let vec(a),vec(b) and vec(c )be three non-coplaner vectors and vec(p),vec(q),vec(r) be three vectors such that vec(p)=2vec(a)-vec(b)+vec(c ),vec(q)=vec(a)-3vec(b)+2vec(c),vec(r)=vec(a)+vec(b)-vec(c ). If [vec(a)vec(b)vec(c)]=2 then [vec(p)vec(q)vec( r)] equals

Answer»

6
-6
3
None of these

Solution :
`"Area of 1 traingle" =(1)/(2)xx2pixxpi=pi^(2)"" "Area of 1 semicircle" =(1)/(2)(pi((1)/(2))^(2))=(pi)/(8)`
`underset(xrarroo)(Lt)(underset(0)overset(x)(int)F(t)DT)/(underset(0)overset(x)(int)G(t)dt)=underset(xrarroo)(Lt)(pi^(2).[(x)/(2pi)]+underset([(x)/(2pi)])overset((x)/(2pi))(int)COS^(-1)(COSX)dx)/((pi)/(8)[x]+underset([x])overset(x)(int)sqrt({x}-{x}^(2)).dx)`
`underset(xrarroo)(Lt)(pi^(2)((x)/(2pi))-pi^(2).{(x)/(2pi)}+int)/((pi)/(8)x-(pi)/(8){x}+int)=underset(xrarroo)(Lt)((pi)/(2)+(("finite quantity"))/(x))/((pi)/(8)+(("finite quantity"))/(x))=((pi//2))/((pi//8))=4`


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