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Locus of the mid-points of all chords of the parabola `y^(2)=4ax` which are drwan through the vertax is a parabola, then its latus rectum isA. `(a)/(2)`B. aC. 2aD. `(3a)/(2)` |
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Answer» Correct Answer - B The unit vectors in the direction of the given vectors are `(6hat(i)+2hat(j)+3hat(k))/(sqrt(36+4+9))=(6hat(i)+2hat(j)+3hat(k))/(7),(3hat(i)-2hat(j)+6hat(k))/(7)" and "(2hat(i)-3hat(j)-6hat(k))/(7)` Since `F_(1),F_(2)" and "F_(3)` are the forces of magnitude 5,3 and 1 units, we have `F_(1)=(5)/(7)(6hat(i)+2j+3k)` `F_(2)=(3)/(7)(3i-2j+6k)" and "F_(3)=(1)/(7)(2i-3j-6k)` Therefore the resultant is `R=F_(1)+F_(2)+F_(3)=(1)/(7)(41i+j+27k)" and " AB=3i+4k`. Hence the work done is `vec(R).vec(AB)=(1)/(7)(41xx3+27xx4)=(231)/(7)=33" units"`. |
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