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bar(a) and bar(b) are non-collinear vect...

`bar(a)` and `bar(b)` are non-collinear vectors. If `bar(c)=(x-2)bar(a)+bar(b)` and `bar(d)=(2x+1)bar(a)-bar(b)` are collinear, then find the value of x.

Text Solution

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Since `bar(c)` and `bar(d)` are collinear vectors, there exists scalar t such that
`bar(c)=tbar(d)`
`:.(x-2)bar(a)+bar(b)=t[(2x+1)bar(a)-bar(b)]`
`:.(x-2)bar(a)+bar(b)=t(2x+1)bar(a)-tbar(b)`
`:.x-2=t(2x=1)` and `1=-t`
`:.t=-1`
`:.x-2=-(2x+1)=-2x-`
`:.3x=1" ":.x=(1)/(3)`.
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