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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 .
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What is the product of two vector quantities?
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.
Why the product of two vectors is sometime scalar and sometime 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.
If a and b are two vectors and the vector product of vector a and vector b is equal to a minus b then prove that a equals b?
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 the vector product of two vectors is zero?
When they point in the same direction.
Why is magnetic field vector a pseudo vector?
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).
How the cross product of two vector is negative?
The cross product of two vectors can result in a negative vector if the two original vectors are not parallel to each other and the resulting vector points in the direction opposite to what is conventionally defined as the right-hand rule direction. In essence, the orientation of the resulting vector determines if it is negative or positive.
What is the product of two vector quantities?
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.
What is the difference between scalar and vector products of two vectors?
The scalar product (dot product) of two vectors results in a scalar quantity, representing the magnitude of the projection of one vector onto the other. The vector product (cross product) of two vectors results in a vector quantity that is perpendicular to the plane formed by the two input vectors, with a magnitude equal to the area of the parallelogram they span.
Why the product of two vectors is sometime scalar and sometime 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.
What is scalar and vector product simplify?
Scalar product (or dot product) is the product of the magnitudes of two vectors and the cosine of the angle between them. It results in a scalar quantity. Vector product (or cross product) is the product of the magnitudes of two vectors and the sine of the angle between them, which results in a vector perpendicular to the plane containing the two original vectors.
If a and b are two vectors and the vector product of vector a and vector b is equal to a minus b then prove that a equals b?
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...
Is the cross product vector or scalar?
The cross product is a vector. It results in a new vector that is perpendicular to the two original vectors being multiplied.
When the vector product of two vectors is zero?
When they point in the same direction.
Why is magnetic field vector a pseudo vector?
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).
Can a scalar product by a negative quantity?
Yes, a scalar product can be negative if the angle between the two vectors is greater than 90 degrees. In this case, the dot product of the two vectors will be negative.
What is the value of scalar product of two vectors A and B where value of vector A and B is not zero and vector product of two vectors A and B is not zero?
Scalar product = (magnitude of 'A') times (magnitude of 'B') times (cosine of the angle between 'A' and 'B')
What is the product of vector and scalar?
The product of a vector and a scalar is a new vector whose magnitude is the product of the magnitude of the original vector and the scalar, and whose direction remains the same as the original vector if the scalar is positive or in the opposite direction if the scalar is negative.
