InterviewSolution
Saved Bookmarks
InterviewSolution
| 1. |
The position vectors of points A,B and C are `hati+hatj,hati + 5hatj -hatk and 2hati + 3hatj + 5hatk`, respectively the greatest angle of triangle ABC isA. `120^(@)`B. `90^(@)`C. `cos^(-1)(3//4)`D. none of these |
|
Answer» Correct Answer - b Since `vec(OA) = hati +hatj + hatk` ` vec(OB) = hati + 5hatj -hatk` `vec(OC) = 2hati + 3hatj + 5hatk` ` a = BC |vec(BC)|= |vec(OC) - vec(OB)|` `|hati - 2hatj + 6hatk| = sqrt41` `b = CA= |vec(CA)|= |vec(OA) -vec(OC)|` ` = | -hati - 2hatj - 4hatk| = sqrt21` `and c= AB= |vec(AB)| = |vec(OB)-vec(OA)|` `|0 hati + 4hatj - 2hatk| =sqrt20` Since `a gt b gt c`, A is the greatest angle l. therefore, ` cos A = (b^(2) + c^(2)-a^(2))/2bc) = (21 + 20 -41)/(2. sqrt21 . sqrt20) = 0` `angleA = 90^(@)` |
|