InterviewSolution
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InterviewSolution
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Find the angle between the line `vecr=(hati+2hatj-hatk)+lamda(hati-hatj+hatk)` and the plane `ver.(2hati-hatj+hatk)=4` |
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Answer» We know that if `theta` is the angle between the lines `vecr=veca+lamdavecb and vecr*vecn=p`, then `sintheta=|(vecb*vecn)/(|vecb||vecn|)|` Therefore, if `theta` is the angle between `vecr=hati+2hatj-hatk+lamda(hati-hatj+hatk) and vecr*(2hati-hatj+hatk)=4,` then `" "sin theta=|((hati-hatj+hatk)*(2hati-hatj+hatk))/(|hati-hatj+hatk||2hati-hatj+hatk|)|` `" "=(2+1+1)/(sqrt(1+1+1)sqrt(4+1+1))` `" "=(4)/(sqrt(3)sqrt(6))=(4)/(3sqrt2)` or `" "theta=sin^(-1)((4)/(3sqrt2))` |
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