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What is the angle in which the dot product of two non zero vectors is equal?
It depends on what the dot product is meant to be equal to.
What is the least number of non-zero vectors that can be added to give a resultant equal to zero?
Two - if you add two vectors of equal magnitude but in opposite directions, the resultant vector is zero.
Can the sum of two equal vectors be equal to either of the vectors?
Only if one of them has a magnitude of zero, so, effectively, no.
Dot product of two vectors is equal to cross product what will be angle between them?
(A1) The dot product of two vectors is a scalar and the cross product is a vector? ================================== (A2) The cross product of two vectors, A and B, would be [a*b*sin(alpha)]C, where a = |A|; b = |B|; c = |C|; and C is vector that is orthogonal to A and B and oriented according to the right-hand rule (see the related link). The dot product of the two vectors, A and B, would be [a*b*cos(alpha)]. For [a*b*sin(alpha)]C to equal to [a*b*cos(alpha)], we have to have a trivial solution -- alpha = 0 and either a or b be zero, so that both expressions are zeroes but equal. ================================== Of course one is the number zero( scalar), and one is the zero vector. It is a small difference but worth mentioning. That is is to say if a or b is the zero vector, then a dot b must equal zero as a scalar. And similarly the cross product of any vector and the zero vector is the zero vector. (A3) The magnitude of the dot product is equal to the magnitude of the cross product when the angle between the vectors is 45 degrees.
Can three vectors of equal magnitude be combined to give a zero resultant?
Yes, put the three vectors in a plane, with a separation of 120 degrees between each vector and each of the other vectors.
