no .....the scalar product of two vectors never be negative
Yes it can If A is a vector, and B = -A, then A.B = -A2 which is negative. Always negative when the angle is between the vectors is obtuse.
Sure! The vector (cross) product involves the sine of the angle between the
first and second vectors. If the angle going counterclockwise from the first
to the second one is more than 180°, then its sine is negative, and so is the
cross-product.
Of course, in that case there's always an angle that's less than 180° ... if you go
counterclockwise from the second vector to the first. You get the same product of
the magnitudes that way, and the same 'sine', but with the opposite 'sign'. That's
exactly correct: The cross-product of two vectors has two equal and opposite values,
depending on the order in which you do it.
For example think of the 3 unit vectors in the x, y and z directions, usually called i, j and k where k = i X j (sometimes all written in Bold). Then j X i = -k .
It depends on the type of product used. A dot or scalar product of two vectors will result in a scalar. A cross or vector product of two vectors will result in a vector.
Because there are two different ways of computing the product of two vectors, one of which yields a scalar quantity while the other yields a vector quantity.This isn't a "sometimes" thing: the dot product of two vectors is always scalar, while the cross product of two vectors is always a vector.
The question is not correct, because the product of any two vectors is just a number, while when you subtract to vectors the result is also a vector. So you can't compare two different things...
When they point in the same direction.
It is the cross product of two vectors. The cross product of two vectors is always a pseudo-vector. This is related to the fact that A x B is not the same as B x A: in the case of the cross product, A x B = - (B x A).
It depends on the type of product used. A dot or scalar product of two vectors will result in a scalar. A cross or vector product of two vectors will result in a vector.
Because there are two different ways of computing the product of two vectors, one of which yields a scalar quantity while the other yields a vector quantity.This isn't a "sometimes" thing: the dot product of two vectors is always scalar, while the cross product of two vectors is always a vector.
The question is not correct, because the product of any two vectors is just a number, while when you subtract to vectors the result is also a vector. So you can't compare two different things...
When they point in the same direction.
It is the cross product of two vectors. The cross product of two vectors is always a pseudo-vector. This is related to the fact that A x B is not the same as B x A: in the case of the cross product, A x B = - (B x A).
Scalar product = (magnitude of 'A') times (magnitude of 'B') times (cosine of the angle between 'A' and 'B')
For two vectors A and B, the scalar product is A.B= -ABcos(AB), the minus sign indicates the vectors are in the same direction when angle (AB)=0; the vector product is ABsin(AB). Vectors have the rule: i^2= j^2=k^2 = ijk= -1.
Cross product also known as vector product can best be described as a binary operation on two vectors in a three-dimensional space. The created vector is perpendicular to both of the multiplied vectors.
I think you meant to ask for finding a perpendicular vector, rather than parallel. If that is the case, the cross product of two non-parallel vectors will produce a vector which is perpendicular to both of them, unless they are parallel, which the cross product = 0. (a zero vector)
The product of scalar and vector quantity is scalar.
The magnitude of dot product of two vectors is equal to the product of first vector to the component of second vector in the direction of first. for ex.- A.B=ABcos@
When performing the cross product of two vectors (vector A and vector B), one of the properites of the resultant vector C is that it is perpendicular to both vectors A & B. In two dimensional space, this is not possible, because the resultant vector will be perpendicular to the plane that A & B reside in. Using the (i,j,k) unit vector notation, you could add a 0*k to each vector when doing the cross product, and the resultant vector will have zeros for the i & jcomponents, and only have k components.Two vectors define a plane, and their cross product is always a vector along the normal to that plane, so the three vectors cannot lie in a 2D space which is a plane.