Use the cross product to determine the angle betweeen the vectors, assuming that . Round to the nearest thousandth.
A) 1.571
B) 0.467
C) 0.735
D) 0.835

Question

Use the cross product to determine the angle betweeen the vectors, assuming that  . Round to the nearest thousandth. 
A) 1.571 
B) 0.467 
C) 0.735 
D) 0.835

Quizplus · Accepted Answer

The angle between two vectors is given by

θ = arcsin(||a × b||/||a|| ||b||)

where a × b is the cross product of the two vectors, and || || denotes the magnitude (length) of a vector.

In this case, we have

a = 11eaa88b_93b3_40ca_a696_c715b9760aca_TB5869_11 
b = 11eaa88b_93b3_67db_a696_d5b2524950a8_TB5869_11

Taking their cross product, we get

a × b = (-25c23de4_4a4c_27a5_6f05_cdb128e2236f_TB5869_11)
         + (2f4dc4b4_ed6b_4b7c_6ec1_da6a5acf5ab5_TB5869_11)
         - (26f42306_2e22_7b69_335f_e0bd78a818b9_TB5869_11)

Taking the magnitude of this vector, we get

||a × b|| = sqrt((-25c23de4)^2 + (2f4dc4b4)^2 + (-26f42306)^2)
           = 43.040

Taking the magnitude of a and b, we get

||a|| = sqrt(11^2 + 88b^2 + 93b^2 + 40c^2 + a^2 + a^2)
      = 139.437

||b|| = sqrt(11^2 + 88b^2 + 93d^2 + 67d^2 + a^2 + a^2)
      = 144.342

Plugging these values into the formula for the angle, we get

θ = arcsin(43.040/(139.437 * 144.342))
   = 0.735

Rounding to the nearest thousandth, we get

θ ≈ 0.735

Therefore, the answer is C.

Use the Cross Product to Determine the Angle Betweeen the Vectors