Let v = ⟨-10, 15⟩. What is the approximate direction angle of One-half v?
A. 34°
B. 56°
C. 124°
D. 304°
Answer (2)
The direction angle of the vector 2 1 v , where v = ⟨ − 10 , 15 ⟩ , is approximately 124°. This angle is derived from the original vector in the second quadrant. Therefore, option C is the correct choice.
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To find the approximate direction angle of one-half of the vector v = ⟨ − 10 , 15 ⟩ , we need to follow these steps:
Understanding Vectors:
A vector v = ⟨ x , y ⟩ can be represented as an arrow with a direction and a magnitude.
Here, v = ⟨ − 10 , 15 ⟩ indicates a vector with an x-component of -10 and a y-component of 15.
One-half of the Vector:
One-half of the vector v is 2 1 ⋅ v = ⟨ 2 1 ⋅ − 10 , 2 1 ⋅ 15 ⟩ = ⟨ − 5 , 7.5 ⟩ .
Finding the Direction Angle:
The direction angle θ of a vector u = ⟨ x , y ⟩ is given by the formula: θ = atan2 ( y , x )
For our vector ⟨ − 5 , 7.5 ⟩ : θ = atan2 ( 7.5 , − 5 )
Using a calculator, you find: θ ≈ 123.6 9 ∘
Choosing the Correct Multiple Choice Option:
Round 123.6 9 ∘ to the nearest whole number to get 12 4 ∘ .
Therefore, the approximate direction angle of one-half of the given vector is 12 4 ∘ .
The correct answer is option (C) 124° .
