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Question

Write down a unit vector in XY- plane, making an angle of 30 in anticlockwise direction with the positive direction of X-axis.


Solution



Let OP make 30 with X-aixs, 60 with Y-axis and 90 with Z-axis and it lies in XY-plane.
Direction cosines of OP are cos 30, cos 60 and co 90 i.e.,32,12,0. Thus,OP is 32 ^i+12 ^j,
|OP|=(322)+(12)2=34+14=1=1
which is required unit vector in XY-plane.

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