InterviewSolution
Saved Bookmarks
InterviewSolution
| 1. |
If `A ,B ,C ,D`are four distinct point inspace such that `A B`is not perpendicular to `C D`and satisfies ` vec A Bdot vec C D=k(| vec A D|^2+| vec B C|^2-| vec A C|^2=| vec B D|^2),`then find the value of `kdot` |
|
Answer» Let A be the origin, and the position vectors of B,C and D be `vecb,vecc,vecd` `vec(AB).vec(CD)=k(|vec(AD)|^(2)+|vec(BC)|^(2)-|vec(AC)|^(2)-|vec(BD)|^(2))` or ` (vecb).(vecd - vecc)` `k = [(vecd)^(2)+(vecc-vecb)^(2)-(vecc)^(2)- (vecd-vecb)^(2)]` `or vecb.vecd-vecc=k (-2vecb.vecc+ 2vecb .,vecd)` or k 1/2 |
|