Question

Find the vectors that join the center of a clock to the hours 1:00, 2:00, and 3:00. Assume the clock is circular with a radius of 1 unit

Answer 1

Consider the clock given in the figure shows.

The angle made by vectors joining the centre and 1, 2, and 3 and the positive x-axis are as follows:

OA with x-axis=60^o

OB with x-axis=30^o

OC with x-axis=0⁰

vector OA =$1cos60^oi+1sin60^oj$

at 1 we have $1/2i+\sqrt{3}/2j$

vector OB =$1cos30^oi+1sin60^oj$

at 2 we have $\sqrt{3}/2i$ $+1/2j$

vector OC =$1cos0 i+1sin0 j=i+0j=i$ (at 3:00)