hi , I have a problem about vector coordinates. this is the problem: We have a 2-dimension space [x(unit vector i) and y( unit vector j)]. I have a circle of center 0 (0,0) and a point P such that OP = r. Vector OP and the x-axis have an angle of θ . there is a unit vector ir , with the same direction with OP( but starting at P.) Another unit vector it starts at P , but vector it is perpendicular to vector ir. (vector it 's direction is toward north-west) Express vector ir as a combination of unit vectors i and j. Express vector it as a combination of unit vectors i and j. I found that ir = cos(θ ) i + sin(θ ) j how to find it ? when I try to compute for vector it, I found the same as vector ir, but I am not sure. Please help Thank you
Hi there im not quite clear on what is being asked but to state a vector in terms of its components you need to do the following. Let x -axis be the i component and y - axis be j component. Look on your graph and see where the tip of the vector touches in terms of its coordinates ( x,y), now the value of x say it was 2 you would write 2i, then say the y axis coordinate was 3 you would write 3j, putting it together you would write that your vector with it's magnitude and direction is equal to 2i +3j.
Hi there, As the unit vector it is perpendicular to the unit vector ir so its angle with the x-axis is 90+theta.Substituting this value in expression for ir we get it=cos(90+theta)i+sin(90+theta)j or it =-cos(theta)i+sin(theta)j As cos(90+theta)=-cos(theta) and sin(90+theta)=sin(theta). I hope this solves your problem. Thank you