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The general idea is that 3 vectors are in a plane iff they are not linearly independent. This can be checked in several ways:
- guessing a way to represent one of them as a linear combination of the other two - if it can be done, then they are coplanar;
- if they are three-dimensional, simply by calculating the determinant of the matrix whose columns are the vectors - if it's zero, they are coplanar, otherwise, they aren't;
- otherwise, you may calculate the determinant of their gramian matrix, that is, a matrix whose ij-th entry is the dot product if the i-th and j-th of the three vectors (e.g. it's 1-2-nd entry would be the dot product of first and second of them); they are coplanar iff the determinant is zero.
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Can three vectors not in one plane give zero resultant?
No. For three vectors they must all lie in the same plane. Consider 2 vectors first. For them to resolve to zero, they must be in opposite direction and equal magnitude. So they will lie along the same line. For 3 vectors: take two of them. Any two vectors will lie in the same plane, and their resultant vector will also lie in that plane. Find the resultant of the first two vectors, and the third vector must be along the same line (equal magnitude, opposite direction), in order to result to zero. Since the third vector is along the same line as the resultant vector of the first two, then it must be in the same plane as the resultant of the first two. Therefore it lies in the same plane as the first two.
What is the Smallest magnitude of sum of 4 and 3 meter vectors?
The smallest magnitude resulting from the addition of vectors with individual magnitudes of 4 and 3 is 1, obtained when the directions of the two component vectors are 180 degrees apart.
Is it possible to add three vectors of equal magnitudes and get zero?
Of course it is! for example, [1, √3] + [-2, 0] + [1, - √3 ] = [0, 0]. Like this example, all other sets of such vectors will form an equilateral triangle on the graph.. Actually connecting the endpoints of the 3 vectors forms the equilateral triangle. The vectors are actually 120° apart.
What are 3 measurements of vectors?
2 inches, 3 inches, and 4 inches
When two nonzero vectors A and B are added and the sum has magnitude 3 it's possible that A equals B equals 3?
The vectors can not be both equal, but they can have the same magnitude of 3, if they are at a 60 degree angle.
