Use a scientific calculator to find the cosine of each of the three angles. For example, given Ax = 34.2, Ay = 116.0 and Az = 69.4, where Ax, Ay and Az are the angles with respect to the x-, y- and z-axes, the cosines are:
cos(34.2) = 0.827
cos(116.0) = -0.438
cos(69.4) = 0.352
Calculate the unit-vector coefficients by multiplying each of the cosines times the magnitude of the vector: Q = M*cos(Ax), R = M*cos(Ay) and S = M*cos(Az), where Q, R and S are the coefficients, and M is the magnitude. Unit vectors are vectors with a magnitude of one. Multiplying a unit vector times a coefficient results in a vector pointing in the same direction as the unit vector but with a magnitude equal to the coefficient. For example, if the magnitude is 10, the coefficients are:
Q = 10*0.827 = 8.27
R = 10*(-0.438) = -4.38
S = 10*0.352 = 3.52
Write the vector in the form Qi + Rj + Sk, where i, j and k are the unit vectors pointing in the directions of the positive x-, y- and z-axes, respectively. A shorthand way of writing vectors is to put their coefficients in parenthesis like (Q, R, S). The coefficients are called the vector's components. For example, write the vector as 8.27i - 4.38j + 3.52k or with the shorthand notation (8.27, -4.38, 3.52).