Q14 of 73 Page 440

Show that the vector is equally inclined to the axes OX, OY and OZ.

To find the inclination of the vector with OX, OY, OZ. We find the direction cosines of the vector.


We know that the direction cosines of a vector are defined as the coefficients of in the unit vector in the direction of the vector.


So, first we find the unit vector in the direction of the vector.


Let




Therefore, The direction cosines of the given vector are .


Let be the angle between and OX.


Therefore,



Similarly, Let be the angle between and OY.


Therefore,



And, be the angle between and OZ.


Therefore,



Therefore,


Hence proved that the vector is equally inclined with the axes OX, OY, and OZ.


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