2022-01-03 18:34:08
Revision Notes on Vectors
Some Basic Results of Vector Calculus:
1) Vectors in the same direction can be added by simply adding their magnitudes. But if the vectors to be added are in opposite directions, then their magnitudes are subtracted and not added.
2) Column vectors can be added by simply adding the values in each row.
3) You can find the magnitude of a vector in three dimensions by using the formula a2 = b2 + c2 + d2, where a is the magnitude of the vector, and b, c, and d are the components in each direction.
4) If l1a + m1b = l2a + m2b then l1 = l2 and m1 = m2
5) Collinear Vectors are also parallel vectors except that they lie on the same line.
6) When two vectors are parallel, the dot product of the vectors is 1 and their cross product is zero.
7)Two collinear vectors are always linearly dependent.
8) Two non-collinear non-zero vectors are always linearly independent
9) Three coplanar vectors are always linearly dependent.
10) Three non-coplanar non-zero vectors are always linearly independent
11) More than 3 vectors are always linearly dependent.
12) Three vectors are linearly dependent if they are coplanar that means any one of them can be represented as a linear combination of other two.
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