Find the angle between vector bold lower u equals 3 bold lower I plus start root 3 end root bold lower j and vector bold lower v equals negative 2 bold lower I minus 5 bold lower j to the nearest degree.

Question

(1 point)
Responses

82°

82°

38°

38°

142°

142°

98°
98°

Answer 1

To find the angle between two vectors, we use the dot product formula:

θ = arccos((u • v) / (||u|| * ||v||))

Given u = 3i + √3j and v = -2i - 5j, we can calculate the dot product:

u • v = (3*-2) + (√3*-5) = -6 - 5√3
||u|| = √(3^2 + (√3)^2) = √12
||v|| = √(2^2 + 5^2) = √29

Plugging these values into the formula:

θ = arccos((-6 - 5√3) / (2√3 * √29))
θ = arccos((-6 - 5√3) / (2√87))

Approximating the angle to the nearest degree gives us:

θ ≈ 98°

Therefore, the angle between vector u and vector v is approximately 98°.