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The magnitude of the projection of the vector `2hati+3hatj+hatk` on the vector perpendicular to the plane containing the vectors `hati+hatj+hatk" and "hati+2hatj+3hatk`, isA. `sqrt(3)/(2)`B. `sqrt(6)`C. `3sqrt(6)`D. `sqrt((3)/(2))` |
Answer» Correct Answer - D The normal vector to the plane containing the vecotors `(hati+hatj+hatk)" and "(hati+2hatj+3hatk)` is `n=(hati+hatj+hatk)xx(hati+2hatj+3hatk)` `=|{:(hati,hatj,hatk),(1,1,1),(1,2,3):}|` `=hati(3-2)-hatj(3-1)+hatk(2-1)=hati-2hatj+hatk` Now, magnitude of the projection of vector `2hati+3hatj+hatk` on normal vector n is `(|(2hati+3hatj+hatk).n|)/(|n|)=(|(2hati+3hatj+hatk).(hati-2hatj+hatk)|)/(sqrt(1+74+1))` `=(|2-6+1|)/(sqrt(6))=(3)/(sqrt(6))=sqrt((3)/(2))`units |
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