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How do you prove that the diagonals of a rectangle are congruent using vectors?
If the vectors emanting from one corner of the rectangel are called a and b then. (a) + (b) = one diagonal (a) + (-b) = the other diagonal and |(a) + (b)| = |(a) + (-b)| (the absolute value of the diagonal's scalars are equal)
Can the resultant of two vectors of the same magnitude be equal to the magnitude of either of the vectors?
Magnitude? Yes. Simple answer: think of it as a triangle. Can a triangle have three sides of the same length? Yes. Long answer: there really isn't a long answer. To get the resultant of two vectors, one would add up the components of each vector. While it is impossible to add two vectors of the same magnitude and derive a resultant of the same magnitude AND DIRECTION as one of the vectors, one need only to create a directional difference of exactly 60 degrees between the first two vectors to result in a resultant of like magnitude. Math really is the most perfect language. Vectors are to triangles what optics are to to the study of conics!
Two vectors of equal magnitude have got a resultant whose magitude is equal to either one of them. Find the angle between the two vectors?
120 deg
What is the difference between zero and vector zero?
The zero vector occurs in any dimensional space and acts as the vector additive identity element. It in one dimensional space it can be <0>, and in two dimensional space it would be<0,0>, and in n- dimensional space it would be <0,0,0,0,0,....n of these> The number 0 is a scalar. It is the additive identity for scalars. The zero vector has length zero. Scalars don't really have length. ( they can represent length of course, such as the norm of a vector) We can look at the distance from the origin, but then aren't we thinking of them as vectors? So the zero vector, even <0>, tells us something about direction since it is a vector and the zero scalar does not. Now I think and example will help. Add the vectors <2,2> and <-2,-2> and you have the zero vector. That is because we are adding two vectors of the same magnitude that point in opposite direction. The zero vector and be considered to point in any direction. So in summary we have to state the obvious, the zero vector is a vector and the number zero is a scalar.
When adding vectors in one dimension what does the length of arrows represent?
The magnitudes of the vectors. apexs
