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Can a vector space have exactly two distinct vectors in it?
No.A vector space is a set over a field that has to satisfy certain rules, called axioms. The field in question can be Z2 (see discussion), but unlike a field, a vector's inverse is distinct from the vector. Therefore, in order to satisfy the "inverse elements of addition" axiom for vector spaces, a vector space must minimally (except if it is the null space) have three vectors, v, 0, and v-1. The null space only has one vector, 0.Field's can allow for two distinct elements, unlike vector spaces, because for any given element of a field, for example a, a + (-a) = 0 meets the inverse axiom, but a and -a aren't required to be distinct. They are simply scalar magnitudes, unlike vectors which can often be thought of as having a direction attached to them. That's why the vectors, v and -v are distinct, because they're pointing in opposite directions.
Can a vector be represented in terms of unit vector?
Yes, a vector can be represented in terms of a unit vector which is in the same direction as the vector. it will be the unit vector in the direction of the vector times the magnitude of the vector.
How will you get the resultant of all vectors?
Graphical Vector AdditionDraw your first vector. Then draw the tail (start) of your second vector at the tip (end) of your first vector. Then draw the tail of your third vector at the tip of you third vector (if it exists,) and so on. To find the resultant, draw a vector from the tail of the first vector to the tip of the last vector. The angle of the resultant will be between the resultant's tail and the first vector's tail. To find these values, it is recommended that you use a scale (e.g. 1cm:1m) and a protractor so that your values are accurate.Or, to do it mathematically (with 2 vectors):You have vector a with angle Ao, and vector b with angle Bo.To get vector c (resultant,) break the vectors up into their x and y components, then add the x and y components to find the x and y of the resultant. To find the magnitude of vector c, use Pythagoras's theorem, a2 + b2 = c2. To find the angle of c, use inverse tangent, tan-1(y/x)Example:Remember that sin = y and cos = x. Thus, to find the x component of a vector, use cos, and to find the y component of a vector, use sin.c = square root( (acosA + bcosB)2 + (asinA + bsinB)2 )angle of c = tan-1( (asinA + bsinB)/(bcosA + bcosB) )
Definition of Inverse property of addition?
* *It is the reverse of the actionEx.Addition is the inverse of subtrationmultiplication is the inverse of division
What are the two sets of inverse operations?
Addition is the inverse operation of subtraction and multiplication is the inverse operation of division. The word inverse means "opposite".
