Solve problems using i, j and k unit vectors

Understanding i, j, and k Unit Vectors

i, j, and k are standard unit vectors in 3D space representing the x, y, and z dimensions respectively.
A unit vector has a magnitude (or length) of one and describes a direction.
Unit vectors can be used to represent any vector in space through a directed line segment.
The direction of i is along the x-axis, j along the y-axis, and k along the z-axis, while their magnitudes are all equal to 1.

The position vector of a point (x, y, z) in 3D space can be represented as xi + yj + zk.
To represent a vector in 3D space, the relevant coefficients of the unit vectors i, j, and k are found, effectively breaking down the vector into its components along the axes.
A vector operation (like addition, subtraction, etc.) can be carried out by performing the operation on the individual components of the vectors.
Scalar multiplication can be carried out by multiplying each component of the vector by the scalar.

To add or subtract vectors, add or subtract the corresponding components. If A = ai + bj + ck and B = di + ej + fk, then A + B = (a+d)i + (b+e)j + (c+f)k.
Dot product of two vectors A and B is calculated by multiplying the corresponding components and adding them up: A.B = ai.bj + aj.bj + ak.bk.
The cross product of two vectors results in a third vector that is perpendicular to the plane containing the first two vectors. If A = ai + bj + ck and B = di + ej + fk, then A x B = (bf - ce)i - (af - cd)j + (ae - bd)k.
To find the magnitude of a vector represented with unit vectors, square each of the component, add them up, and take the square root.
To find the angle between two vectors, use the dot product formula: A.B = A B cos(theta), where theta is the angle between A and B.
When tackling physics problems, use i, j, and k to represent forces, velocities, and accelerations in their respective components along the axes. Then apply the appropriate vector or scalar operation.