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Let bar a = 2bar i +bar j+bar k, bar b ...

Let `bar a = 2bar i +bar j+bar k, bar b =bar i+2bar j -bar k` and a unit vector `bar c` be coplanar. If `bar c` is perpendicular to `bar a` , then `bar c` is

A

`1/sqrt2(-j+k)`

B

`1/sqrt3(i-j-k)`

C

`1/sqrt5(i-2j)`

D

`1/sqrt3(i-j-k)`

Text Solution

Verified by Experts

As `vecc` is coplanar with `veca and vecb` we take
`vecc = alpha veca + betavecb`
where `alpha and beta` are scalars.
As `vecc` is perpendicular to `veca` , using (i), we get
`0 = alphaveca.veca alpha +betavecb.veca`
`or 0 =alpha (6) +beta(2+2-1) =3 (2alpha+beta) `
`or beta = -2alpha`
Thus `vecc=alpha(veca -2vecb)=alpha(-3j+3k)=3alpha(-j+k)`
`or |vecc|^(2)=18alpha^(2)`
`or 1=18alpha^(2)`
`or alpha= +- 1/(3sqrt2)`
`vecc =+- 1/sqrt2 (-j+k)`
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