When the angle between two vectors is zero ... i.e. the vectors are parallel ... their sum is a vector in the
same direction, and with magnitude equal to the sum of the magnitudes of the two original vectors.
Chat with our AI personalities
It depends on what the dot product is meant to be equal to.
Only if one of them has a magnitude of zero, so, effectively, no.
Two - if you add two vectors of equal magnitude but in opposite directions, the resultant vector is zero.
(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.
Yes, put the three vectors in a plane, with a separation of 120 degrees between each vector and each of the other vectors.