Find the magnitude and direction (in degrees) of the vector. assuming 0 ≤ θ < 360.?

Question

v=2i+2(squareroot 3) j

|v|= 

θ =

Answer 1

v = 2i + 2√3 j

The magnitude of vector is |v| = √ (a² + b²)    if the vector is a i + b j .

|v| = √ (2² + (2√3)²) 

|v| = √ (4 + 4*3) 

|v| = √ (4 +12) 

|v| = √16

|v| = 4 

So the magnitude of vecor is 4 .

To find the direction or angle, we use the formula that θ = arctan(b/a) 

 θ = arctan (2√3 / 2)

 θ = arctan (√3)

 θ = 60°

The angle or the direction of vector is θ = 60° .