Question

Find the angle between the given vectors to the nearest tenth of a degree. mathbfu = ⟨ 6, 4 ⟩, mathbfv = ⟨ 7, 5 ⟩ .

a) 29.7°
b) 35.1°
c) 41.2°
d) 48.4°

Answer 1

To find the angle between two vectors, you can use the dot product formula. In this case, the angle between vectors u and v is approximately 29.7°.

Step-by-step explanation:

To find the angle between two vectors, you can use the dot product formula. Let's call the angle between vectors u and v as theta. The dot product of u and v is given by u.v = |u||v|cos(theta).

In this case, u = ⟨6, 4⟩ and v = ⟨7, 5⟩.

The magnitude of u is sqrt(6^2 + 4^2) = 2sqrt(13) and the magnitude of v is sqrt(7^2 + 5^2) = sqrt(74).

Plugging these values into the dot product formula, we have 6*7 + 4*5 = (2sqrt(13))*(sqrt(74))*cos(theta).

Solving for cos(theta), we get cos(theta) = 62/(2sqrt(13)*sqrt(74)).

Taking the arccosine of both sides, we find theta ≈ 29.7°.

Therefore, the correct answer is (a) 29.7°.