Find the angle between the vectors u and v if and Round your answer to two decimal places.
A)66.14°
B)68.34°
C)67.38°
D)65.45°
E)68.79°

Question

Find the angle between the vectors u and v if  and  Round your answer to two decimal places.
A)66.14° 
B)68.34° 
C)67.38° 
D)65.45° 
E)68.79°

Quizplus · Accepted Answer

Using the dot product formula, we have:

u · v = ||u|| ||v|| cosθ

where ||u|| and ||v|| are the magnitudes of vectors u and v respectively, and θ is the angle between them.

Calculating the magnitudes, we get:

||u|| = sqrt(11^2 + 1^2 + 11^2) = sqrt(243)
||v|| = sqrt(11^2 + 1^2 + 10^2) = sqrt(242)

Calculating the dot product, we get:

u · v = 11(11) + 1(1) + 11(10) = 243

Substituting all values into the formula, we have:

243 = sqrt(243) sqrt(242) cosθ

Solving for cosθ, we get:

cosθ = 243 / (sqrt(243) sqrt(242)) = sqrt(243/242)

Taking the inverse cosine, we get:

θ = acos(sqrt(243/242)) = 67.38° (rounded to two decimal places)

Therefore, the answer is C.

Find the Angle Between the Vectors U and V If