Saved Bookmarks
| 1. |
Show that the resultant of two vectors vec(A) and vec(B)always lies between A + B andA - B |
|
Answer» Solution :Let `theta ` bethe ANGLE between `VEC(A) and vec(B)`. Thus the resultant of `vec(A) and vec(B)`is given by `vec(R) = sqrt(A^(2) + B^(2) = 2AB cos theta)` (or)`R^(2) = A^(2) + B^(2) + 2AB cos theta` Now greatest value of cos`theta `is + 1 Greatest value of `R^(2) "is" (A^(2) +B^(2) +2AB) or(A+ B)^(2)` i.e., the greatest valure of R is (A + B) The least of `cos theta` is - 1 So the least value of `R^(2) is(A^(2) +B^(2) - 2AB) or (A - B)^(2)`i.e., the least value of R is (A - B) |
|