Please Help!
What is the direction of the vector r of t equals the vector with components square root of 3, 1? (10 points)
A) pi over 6
B) 1
C) the square root of 2
D) pi over 3
did you draw the vector?
tanθ = 1/√3
does that look familiar?
Yes! I did, but I didn't know how to go on from there
I got D as my answer, Is this right? Thank you so much for taking the time to help me!
To find the direction of a vector, we can use the formula:
θ = tan^(-1)(y/x)
where θ represents the angle and (x, y) are the components of the vector.
In this case, the vector has components √3 and 1. So, we can substitute these values into the formula:
θ = tan^(-1)(1/√3)
To evaluate this, we can use a calculator or reference a trigonometric table. The result is approximately 0.615.
Now, to determine which option represents the direction, we need to convert the result to one of the given options:
A) π/6 ≈ 0.524
B) 1 is not an angle
C) √2 ≈ 1.414
D) π/3 ≈ 1.047
Comparing the result 0.615 to the given options, we find that the closest value is option D) π/3.
Therefore, the direction of the vector r of t with components √3 and 1 is approximately π/3.