Determine if , and where θ is the angle between u and v.Round answer to two decimal places.
A)21.21
B)20.49
C)15.00
D)18.11
E)25.98

Question

Determine  if  , and  where θ is the angle between u and v.Round answer to two decimal places.
A)21.21 
B)20.49 
C)15.00 
D)18.11 
E)25.98

Quizplus · Accepted Answer

In order to find the value of 11eacce6_1f15_d4a2_9f49_3f00153aee88_TB7896_11, we need to use the dot product formula:

u · v = |u| |v| cos(θ)

where u = 11eacce6_1f15_d4a3_9f49_3ba55cf73be3_TB7896_11 and v = 11eacce6_1f15_d4a4_9f49_1bb4424e6f6c_TB7896_11

First, we need to find the magnitude of u and v:

|u| = √(11^2 + 3^2 + 5^2) = √155
|v| = √(11^2 + 1^2 + 6^2) = √162

Next, we need to find the dot product of u and v:

u · v = (11)(11) + (3)(1) + (5)(6) = 148

Finally, we can solve for cos(θ):

cos(θ) = (u · v) / (|u| |v|)
cos(θ) = 148 / (√155)(√162)
cos(θ) ≈ 0.866

Therefore, θ ≈ 15.00 degrees.

Now we can use the same formula to find 11eacce6_1f15_d4a2_9f49_3f00153aee88_TB7896_11:

11eacce6_1f15_d4a2_9f49_3f00153aee88_TB7896_11 = |u| |v| sin(θ) cross product of u and v

sin(θ) = √(1 - cos^2(θ))
sin(θ) ≈ 0.500

Finally,

11eacce6_1f15_d4a2_9f49_3f00153aee88_TB7896_11 ≈ (√155)(√162)(0.50)
11eacce6_1f15_d4a2_9f49_3f00153aee88_TB7896_11 ≈ 15.00

Therefore, the best choice is C, 15.00.

Determine If , and Where θ Is