1.

The vertices of a triangle ABC are A-=(2,0,2), B(-1,1,1) and C-=(1,-2,4). The points D and E divide the sides AB and CA in the ratio 1:2 respectively. Another point F is taken in space such that the perpendicular drawn from F to the plane containing DeltaABC, meets the plane at the point of intersection of the line segments CD and BE. If the distance of F from plane of triangle ABC issqrt(2), units, ten

Answer» <html><body><p>the volume of the tetrahdron `ABCD` is `7/3` <a href="https://interviewquestions.tuteehub.com/tag/cubic-940181" style="font-weight:bold;" target="_blank" title="Click to know more about CUBIC">CUBIC</a> units<br/>the volume of the tetrahedron `ABCF` is `7/6` cubic units<br/>one of the equation of the line `AF` is `vecr=(2hati+2hatk)+<a href="https://interviewquestions.tuteehub.com/tag/lamda-536483" style="font-weight:bold;" target="_blank" title="Click to know more about LAMDA">LAMDA</a>(2hatk-hati)(lamda in R)` <br/>one of the equuation of the line `AF` is `vecr=(2hati+2hatk)+mu(hati+7hatk)`</p>Solution :`CD:vecr(hati-2hatj+4hatk)+(lamda)/3(7hatj-7hatk)` <br/> `BE:vecr=(-hati+hatj+k)+(mu)/3(7hati-7hatj+7hatk)` <br/> `P-=(hati-hatj+3hatj)` <br/> Area of tetrahedron `ABCD` <br/> `=1/3` (Area of base triangle) `<a href="https://interviewquestions.tuteehub.com/tag/xx-747671" style="font-weight:bold;" target="_blank" title="Click to know more about XX">XX</a>` height `=7/3` cubic units <br/> `vec(AB)xxvec(AC)=7hatj+7hatk,|vec(<a href="https://interviewquestions.tuteehub.com/tag/pf-1152667" style="font-weight:bold;" target="_blank" title="Click to know more about PF">PF</a>)|=PF=sqrt(2)` units <br/> `vec(PF)=sqrt(2)((7hatj+7hatk)/(sqrt(49+49)))=hatj+hatk=P.V`. of `F-P.V.` of `P` <br/> `P.V.` of `F=hati+4hatk` <br/> Vector equation of `AF` is `vecr=2(hati+hatk)+<a href="https://interviewquestions.tuteehub.com/tag/alpha-858274" style="font-weight:bold;" target="_blank" title="Click to know more about ALPHA">ALPHA</a>(-hati+2hatk)` <br/> <img src="https://d10lpgp6xz60nq.cloudfront.net/physics_images/FIT_JEE_PT3_P1_E01_294_S01.png" width="80%"/></body></html>


Discussion

No Comment Found

Related InterviewSolutions