InterviewSolution
Saved Bookmarks
InterviewSolution
| 1. |
For three non-zero vectors (a, b and c), prove that vector [(a - b) (b - c) (c - a)] = 0 |
|
Answer» = vector (a - b).[{vector(b - c) x (c - a)}] = vector (a - b).[{vector(b x c - b x a - c x c + c x a)}] = vector (a - b).[{vector(b x c - b x a + c x a)}] ......{(vector(c x c) = 0} = vector (a - b).[{vector(b x c + a x b + c x a)}] = vector [{a.(b x c)} + {a.(a x b)} + {a.(c x a)} - {b.(b x c)} - {b.(a x b)} - {b.(c x a)}] = vector [{a.(b x c)} + 0 + 0 - 0 - 0 - {b.(c x a}] = vector [{a.(b x c)} - {b.(c x a)}] = 0 (STP remains same if vectors (a, b, c) are changed in cyclic order) |
|