Question

consider the vecto shown in the diagram
find the i and j components of v in terms of the magnitude of v and theta

Answer 1

can you help me please

Answer 2

Let v = <x, y>

you would use these formulas

x = |v|*cos(theta)
y = |v|*sin(theta)


So say the reference angle theta = 60 degrees and |v| = 5

this would mean

x = 5*cos(60)
x = 5*(0.5)
x = 2.5

y = 5*sin(60)
y = 5*(0.866)
y = 4.33

If you want the vector to be in Q2, then just make the x coordinate negative.

So the vector that has a reference angle of 60 degrees, a magnitude of 5, and is in the 2nd quadrant is < -2.5, 4.33> roughly.

Answer 3

thank you but can we just write it as \[i=-\left| v \right|\cos \theta and j=\left| v \right|\sin\]theta

Answer 4

well i and j are components of a vector

eg: <2, 3> = 2i + 3j

Answer 5

so idk if it makes sense to write it that way

Answer 6

as the question asks for i and j component i thin my way is right what do you think

Answer 7

i'm reading that i and j are really vectors (that sounds familiar)

it turns out that

i = <1, 0>
j = <0, 1>

Answer 8

so i and j are fixed