InterviewSolution
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InterviewSolution
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A non vector `veca` is parallel to the line of intersection of the plane determined by the vectors `hati,hati+hatj` and thepane determined by the vectors `hati-hatj,hati+hatk` then angle between `veca and hati-2hatj+2hatk` is = (A) `pi/2` (B) `pi/3` (C) `pi/6` (D) `pi/4` |
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Answer» Correct Answer - `pi//4 or 3pi//4` A vector normal to the plane containing vectors ` hati and hati + hatz` is `vecp=|{:(hati,hatj,hatk),(1,0,0),(1,1,0):}|=hatk` A vector normal to the plane containing vectors ` hati- hatj, hati + hatk` is `vecq=|{:(hati,hatj,hatk),(1,-1,0),(1,0,1):}|=-hati-hatj+hatk` vector `veca` is parllel to vector `vecp xx vecq` `vecp xx vecq=|{:(hati,hatj,hatk),(0,0,1),(-1,-1,1):}|=hati-hatj` Therefore, a vector in direction of `veca` is `hati - hatj` Now `theta` is the angle between `hata and hati - 2hatj + 2hatk` then `cos theta=+-(1.1+(-1).(-2))/(sqrt(1+1)sqrt(1+4+4))=+-3/(sqrt(2).3)` `Rightarrow +-1/sqrt2 Rightarrow theta=pi/4or (3pi)/4` |
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