InterviewSolution
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InterviewSolution
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Prove that the plane `vecr*(hati+2hatj-hatk)=3` contains the line `vecr=hati+hatj+lamda(2hati+hatj+4hatk).` |
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Answer» To show that `vecr=hati+hatj+lamda(2hati+hatj+4hatk)" "`(i) lies in the plane `vecr* (hati+2hatj-hatk)=3`,`" "`(ii) we must show that each point of (i) lies in (ii). In order words we must show that `vecr` in (i) satisfies (ii) for every value of `lamda`. We have `" "[hati+hatj+lamda(2hati+hatj+4hatk)]*(hati+2hatj-hatk)` `" "=(hati+hatj)*(hati+2hatj-hatk)+lamda(2hati+hatj+4hatk)*(hati+2hatj-hatk)` `" "=(1)(1)+(1)(2)+lamda[(2)(1)+(1)(2)+4(-1)]=3+lamda(0)=3` Hence, line (i) lies in plane (ii). |
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