Why is vector division not possible?

Why is vector division not possible?

For any entity, vectors or scalars, there are only some operations (and a composition of them) which are possible. Division is not a valid operation for vectors because you can not always get a unique vector which, when multiplied to the divisor according to the rules of vector product, will give you the dividend.

Is division possible for two vectors?

We cannot divide two vectors. The definition of a Vector space allows us to add two vectors, subtract two vectors, and multiply a vector by a scalar. Other vector spaces can have other sorts of multiplication like the Exterior product and other wacky things.

Can we divide a vector by a scalar?

Yes, we can divide a vector by scalar. The magnitude of the vector is reduced by the scalar quantity, when divided.

Can you divide by a unit vector?

To find a unit vector with the same direction as a given vector, we divide the vector by its magnitude. If we divide each component of vector v by |v| we will get the unit vector uv which is in the same direction as v.

Can two vectors of same unit and dimension be divided?

Division is not a valid operation for vectors because you can not always get a unique vector which, when multiplied to the divisor according to the rules of vector product, will give you the dividend. Each vectors in 3-D or in 2-D(or in any dimensions) form a vector space.

What is i dot J?

The dot product of two unit vectors is always equal to zero. Therefore, if i and j are two unit vectors along x and y axes respectively, then their dot product will be: i . j = 0.

Is cross product commutative?

The right hand rule for cross multiplication relates the direction of the two vectors with the direction of their product. Since cross multiplication is not commutative, the order of operations is important. Your thumb is now pointing in the direction of the cross product.

Is it possible to divide a vector by two vectors?

As an aside, you can actually divide two vectors. The only question is how do you want to interpret the objects and more importantly the operation. For example, you can map the vectors to an object in a quaternion space quite simply as: $$ phi:V rightarrow H: vec{v} mapsto (0,vec{v}) , $$.

When does vector division make sense?

There are cases where vector division makes sense and is useful. For example, let’s consider Lorentz force on charge that’s moving in magnetic field.

Is it possible to divide by zero in math?

So you cannot divide by anything, there can be some divisions that cannot be defined, but that’s fine – you cannot divide by zero in reals aswell. You just have to understand what you are doing and whether inverse is unique and if it’s definable at all. There are cases where vector division makes sense and is useful.

What is the dot product of two vectors of the same dimension?

The most obvious “•” is the vector dot product, which gives an ordinary number for the dot product of two vectors of the same dimension. The problem is this: if the dimension is two or bigger, you can always find various x’s with b•x=0, vectors at right angles to b.