Find the magnitude and direction angle of the vector v.?
v = 3(cos 100°i + sin 100°j)
how do i solve this? please show steps i do not understand it
- Steve4PhysicsLv 75 years agoFavorite Answer
||v|| = 3
θ = 100°
No calculation is needed.
To understand this you have to understand components.
A vector v with magnitude ||v|| and direction θ has:
x component = ||v||cos(θ)
y component = ||v||sin(θ)
So in component form the vector is written as:
v = ||v||cos(θ)i + ||v||sin(θ)j
which is the same as:
v = ||v|| (cos(θ)i + sin(θ)j)
Matching this, term by term, to v = 3(cos(100°)i + sin(100°)j) it is clear that ||v|| = 3 and θ = 100°.
If you don't know how to resolve a vector into components, it's covered from the basics in the video in the link.Source(s): http://www.youtube.com/watch?v=OBaCUYBdFs8
- 5 years ago
Your angle is 100 degrees
The x-component is 3 * cos(100)
The y-component is 3 * sin(100)
The magnitude is sqrt(x^2 + y^2) = sqrt(9 * cos(100)^2 + 9 * sin(100)^2) = sqrt(9) * sqrt(cos(100)^2 + sin(100)^2) = 3 * sqrt(1) = 3 * 1 = 3
So, if you see this form:
v = R * (cos(t)i + sin(t)j)
Then the magnitude is R and the angle is t. The math is already done for you.