What is the angle between the two vectors A = 3i + 4j and B = 9i + 12j?oGroup of answer choices180o90o0o-90o
Question
What is the angle between the two vectors
A = 3i + 4j
B = 9i + 12j?
Group of answer choices
180°
90°
0°
-90°
Solution
The angle between two vectors A and B can be calculated using the dot product formula:
A.B = |A||B|cosθ
where:
- A.B is the dot product of A and B
- |A| and |B| are the magnitudes of A and B
- θ is the angle between A and B
First, calculate the dot product of A and B:
A.B = (3i + 4j).(9i + 12j) = 39 + 412 = 27 + 48 = 75
Next, calculate the magnitudes of A and B:
|A| = sqrt(3^2 + 4^2) = 5 |B| = sqrt(9^2 + 12^2) = 15
Substitute these values into the dot product formula and solve for θ:
75 = 515cosθ cosθ = 75 / (5*15) cosθ = 1
The angle whose cosine is 1 is 0 degrees. Therefore, the angle between the two vectors A and B is 0 degrees.
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