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 ,

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, 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