Get I; K

The value of i cap × i cap is equal to 0. Hence, the value of i cap × i cap is equal to 0.

i cap and j cap are the unit vectors, i cap represents unit vector in x direction while j cap represents unit vector in y direction and k cap represents unit vector in z direction.

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. Writing vectors in this form can make working with vectors easier.

We can use these properties, along with the cross product of the standard unit vectors, to write the formula for the cross product in terms of components. Since we know that i×i=0=j×j and that i×j=k= j×i, this quickly simplifies to a×b=(a1b2 a2b1)k=|a1a2b1b2|k.

In words, the dot product of i, j or k with itself is always 1, and the dot products of i, j and k with each other are always 0. The dot product of a vector with itself is a sum of squares: in 2-space, if u = [u1, u2] then u u = u12 + u22, in 3-space, if u = [u1, u2, u3] then u u = u12 + u22 + u32.

The i,j notation A vector can be described using i,j notation. A unit vector is a vector of length 1, in Cartesian co-ordinates the unit vectors along the axis are denoted by i and j respectively. Any two-dimensional vector can be written in the form ai+bj.

Dot Products of Vectors. You'll usually do dot product calculations with the vectors in component form. ... In words, the dot product of i, j or k with itself is always 1, and the dot products of i, j and k with each other are always 0.

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. Writing vectors in this form can make working with vectors easier.

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.