If it’s the displacement vector then the i,j,k will have units of length i.e. meters (m). If it’s the force vector then the i,j,k will have units of force i.e. newtons (N). But if you are talking about vectors in math, then they are unitless.

A scalar is defined to be invariant under transformations of the coordinate system. Thus, a vector in one dimension is not a scalar.

A vector is a quantity that has both magnitude, as well as direction. A vector that has a magnitude of 1 is a unit vector. It is also known as Direction Vector….

It makes sense because a unit vector is defined as ‘a vector’ divided by its magnitude. Since we have the same numerical value in numerator and the denominator, a unit vector has a magnitude of 1 unit.

There are three important unit vectors which are commonly used and these are the vectors in the direction of the x, y and z-axes. The unit vector in the direction of the x-axis is i, the unit vector in the direction of the y-axis is j and the unit vector in the direction of the z-axis is k.

k×k = 0. (5) The identities (5) can be memorized using the mnemonic below: That is, the cross product of any two vertices is the third vertex, with the sign determined by the implied direction (positive if counterclockwise, negative otherwise).

Since the cross product must be perpendicular to the two unit vectors, it must be equal to the other unit vector or the opposite of that unit vector. Looking at the above graph, you can use the right-hand rule to determine the following results. i×j=kj×k=ik×i=j.

What will be the cross product of the vectors 2i + 3j + k and 3i + 2j + k? Explanation: The given vectors are parallel to each other. The cross product of parallel vectors is 0 because sin(0) is 0. 11.