InterviewSolution
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InterviewSolution
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Let `vec(alpha)=ahati+bhatj+chatk, vec(beta)=bhati+chatj+ahatk` and `vec(gamma)=chati+ahatj+bhatk` be three coplnar vectors with `a!=b`, and `vecv=hati+hatj+hatk`. Then `vecv` is perpendicular toA. `vecalpha`B. `vecbeta`C. `vecgamma`D. none of these |
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Answer» Correct Answer - a,b,c It is given that `vecalpha, vecb and vecgamma` are coplanar vectors, therefore ` [vecalpha vecbeta vecgamma] =0` `Rightarrow |{:(a,b,c),(b,c,a),(c,a,b):}|=0` ` or 3abc -a^(3) -b^(3) -c^(3) =0` ` or a^(3) +b^(3) +c^(3) -3abc =0` ` or (a + b +C0 (a^(2) +b^(2) + c^(2) -ab -bc-ca)=0` or a+b+c =0 ` [ a^(2) +b^(2) +c^(2)-ab -bc-ca ne 0)` ` Rightarrow vecv. vecalpha = vecv. vecbeta = vecv. vecgamma = 0` Hence, `vecv` is perpendicular to `vecalpha ,vecbeta and vecgamma` |
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