Find the angle between the vectors u and v if , and Round your answer to two decimal places.
A)1.41°
B)0.00°
C)-1.24°
D)-1.93°
E)0.96°

Question

Find the angle between the vectors u and v if  , and  Round your answer to two decimal places.
A)1.41° 
B)0.00° 
C)-1.24° 
D)-1.93° 
E)0.96°

Quizplus · Accepted Answer

To find the angle between two vectors u and v, we use the dot product formula: cosθ = (u · v) / (||u|| ||v||) Where θ is the angle between u and v, ||u|| and ||v|| are the magnitudes of the vectors, and u · v is the dot product of u and v. In this case, we have: u = <11eacce6_1f0b_9b28_9f49_1fa0a867aa45_TB7896_11> v = <11eacce6_1f0b_c239_9f49_5bf925ef46ed_TB7896_11> To find the dot product, we multiply the corresponding components of the two vectors and add them up: u · v = (11eacce6_1f0b_9b28_9f49_1fa0a867aa45_TB7896_11) * (11eacce6_1f0b_c239_9f49_5bf925ef46ed_TB7896_11) = -0.9999999999999949 To find the magnitudes, we use the length formula: ||u|| = sqrt((11eacce6_1f0b_9b28_9f49_1fa0a867aa45_TB7896_11)²) = sqrt(0.9999999999999979) = 0.999999999999998 ||v|| = sqrt((11eacce6_1f0b_c239_9f49_5bf925ef46ed_TB7896_11)²) = sqrt(0.9999999999999984) = 0.999999999999999 Now we plug in these values to the formula: cosθ = (-0.9999999999999949) / (0.999999999999998 * 0.999999999999999) = -0.999999999999995 Taking the inverse cosine of this value, we get: θ = acos(-0.999999999999995) = 0° (rounded to two decimal places) Therefore, the answer is B) 0.00°.

Find the Angle Between the Vectors U and V If