A force is specified by the vector f = (105i + 135j - 175k) n. calculate the angles made by f with the positive x-, y-, and z-axes.

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Mathematics

22 March, 21:45

A force is specified by the vector f = (105i + 135j - 175k) n. calculate the angles made by f with the positive x-, y-, and z-axes.

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Odin · Answer 1

Calculate the direction cosines, and hence find the angles.

unit vector

=/sqrt (105^2+135^2 + (-175) ^2)

=

= (approx.)

Therefore the direction cosines are respectively

0.4291,0.5517,-0.7152, and the angles with the x, y and z-axes are:

acos (0.4291), acos (0.5517), acos (-0.7152)

=64.59, 56.51, and 135.66 degrees respectively.