Find the angle between u and v in radians.
-u = 7i + 6j + 3k, v = 5i + 2j + 6k
A) 1.15
B) 0.98
C) 0.59
D) 1.47

Question

Quizplus · Accepted Answer

The dot product of two vectors u and v is defined as:
u∙v = |u||v|cosθ
where θ is the angle between the two vectors.

Using the formula:
u∙v = (7)(5) + (6)(2) + (3)(6) = 65
|u| = sqrt(7^2 + 6^2 + 3^2) = sqrt(94)
|v| = sqrt(5^2 + 2^2 + 6^2) = sqrt(65)

Substituting these values in the above formula and solving for θ, we get:
cosθ = u∙v / (|u||v|) = 65 / (sqrt(94)sqrt(65)) ≈ 0.5902

Taking the inverse cosine, we get:
θ ≈ 0.985 radians ≈ 0.59 radians (rounded to two decimal places)

Therefore, the answer is choice C, 0.59.

Find the Angle Between U and V in Radians