The direction cosines and direction angles of the vectors will be x/r , y/r , z/r and cos⁻¹(x/r), cos⁻¹(y/r),cos⁻¹(z/r ) respectively.
The cosines of the angles that a given vector, m = xi + yj + zk, makes well with the x, y, and z axes are the direction cosines of that vector.
If a forms the direction angles (which are cosines) with the x, y, and z axes, then the direction cosines of m are cos a, cos b, and cos c in the x, y, and z axes, respectively.
Let the equation be = xi + yj + zk
vector of the equation will be = (x, y, z)
r = length of vector = √(x²+y²+z²)
The direction cosines will be x/r , y/r , z/r
angles will be cos⁻¹(x/r), cos⁻¹(y/r),cos⁻¹(z/r )
Direction cosines will be -x/r , y/r , z/r
Angles will be -
cos⁻¹(x/r), cos⁻¹(y/r),cos⁻¹(z/r )
Consider the dimensional point P. We can derive direction cosines by computing the cosine of any positive (anticlockwise) angles that a position vector makes with the positive x, y, and z-axes, respectively.
These angles are referred to as direction angles. By using direction cosines, it is easy to translate a vector's direction into angles with regard to a reference.
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