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Is it possible to multiply a vector quantity to a scalar quantity?
The product of scalar and vector quantity is scalar.
How torque is vector and work is scalar quantity?
Torque is got by the cross product of two vectors namely force vector and perpendicular radius vector Tau (torque) = r X F But work is got by the scalar product of force vector and displacement vector Hence W = F . S
Why vector quantities are not divisible?
I'll assume you are referring to the inverse of the most common process of vector multiplication, namely the formation of an inner product, also called a scalar product or dot product, between two vectors of the same size. In this operation, vectors with, for example, components (a,b,c,d) and (e,f,g,h) must be pairwise multiplied and summed, to arrive at the scalar result ae + bf + cg + dh. Any two ordinary vectors of matching size (number of components) can be "multiplied" to get an inner product. (There is another kind of multiplication of two 3-vectors called the cross-product, which is sometimes invertible, but because the cross-product only works with two vectors in 3-space, it does not seem useful to discuss the cross-product further in the context of general vector division. Similarly, one could individually multiply the components of the two vectors to get a sort of third vector. Although that operation would be invertible under some conditions, I am not aware of any meaning, or physical significance, for the use of that technique. Since the result of taking the inner product of two vectors is a scalar, that is, a single real number, most of the information about the two vectors is lost during the computation. The only information retained by the inner product is the magnitude of the projection of one vector A onto the direction of another vector B, multiplied by the magnitude of B. But division is the inverse operation of multiplication. In a sense, division undoes the work of a previous multiplication. Since all information about the direction of each vector is discarded during the calculation of an inner product, there is not enough information remaining to uniquely invert this operation and bring back, say, vector A, knowing vector B and the value of the scalar product.
What are different conditions that could make vector product zero?
First of all, you have to define what you mean by "vector product".-- The "dot product" is zero if the vectors are perpendicular, regardless of their magnitudes.-- The "cross product" is zero if the vectors are collinear or opposite, regardless of their magnitudes.-- Perhaps when you say "product", you mean the "result" of two vectors, whicha mathematician or physicist would cal their "sum".The sum of two vectors is zero if their magnitudes are equal and their directionsdiffer by 180 degrees.An infinite number of other possibilities exist for a sum of zero, depending on themagnitudes and directions of two vectors.
How do you find the direction of a cross product vector?
Think of a screw-thread, threaded just like a screw that you might use to screw a hook into a piece of wood. In the US, all woodscrews are manufactured with what's called a "right-hand thread". That means you turn it right to go into the wood, and you turn it left to bring it out of the wood. Now keep that 'right-hand thread' in the back of your mind, and we'll look at a vector cross-product. A cross-product is the new vector you get when you operate on two vectors that you already have. You obviously know the directions of the vectors that you already have, and you're asking "What is the direction of the new vector ?". Well, call the first two vectors 'A' and 'B'. If you do the cross-product (A x B), think of that right-handed screwthread rotating from the 'A' direction to the 'B' direction. What direction did the right-hand thread advance ? That's the direction of the cross-product ! Can you picture the three-dimensional Cartesian coordinate system ? Down at the origin, where the three axes come together, if you draw three little tiny vectors down on the three axes, you'll notice that ( x cross y = z ). This will help you a lot if you ever have to draw the axes properly on a blank sheet of paper. Notice that (B x A) goes in the opposite direction of (A x B), because when you turn a right-hand thread the other way, the screw advances oppositely. Another contributor may improve this answer by describing the "Right Hand Rule", which is another, maybe better, way to get the direction of the cross product. If he is not a total genius at descriptive language, it will confuse you.
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 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).
If the commutative law not hold in cross product then prove it?
Actually The cross product of two vector is a VECTOR product. The direction of a vector product is found by the right hand rule. Consider two vectorsA and B,AxB= CWhere C is the Cross product of A and B, and by right hand rule its direction is opposite to that of BxA that isBxA=-C
Is it possible to multiply a vector quantity to a scalar quantity?
The product of scalar and vector quantity is scalar.
How to you find a vector parallel to two given 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)
Can the vector product of two vectors be negative?
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.
What is the algebraic definition of a cross product?
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.
How do you do cross products?
You need to know that the cross product of two vectors is a vector perpendicular to both vectors. It is defined only in 3 space. The formula to find the cross product of vector a (vector a=[a1,a2,a3]) and vector b (vector b=[b1,b2,b3]) is: vector a x vector b = [a2b3-a3b2,a3b1-a1b3,a1b2-a2b1]
Cross product is not difine in two space why?
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.
What is cross in science?
One type of cross is the cross or vector product of a pair of 3D vectors. If there are two unit vectors that are not parallel, their vector product is a vector that is normal to the plane containing the two vectors, so it's a good way to find that plane. In biological science, cross signifies the mating of two genotypes to produce its progeny. It may be among homozygous or heterozygous parents.
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.
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.
