Answer:
Explanation:
To find the angle θ between two vectors a and b, you can use the dot product formula:
a • b = |a| * |b| * cos(θ)
where:
a • b is the dot product of vectors a and b.
|a| and |b| are the magnitudes (lengths) of vectors a and b, respectively.
θ is the angle between vectors a and b.
You already have a • b = √3.
Now, you need to find the magnitudes of vectors a and b:
The magnitude of vector a is |a| = √(a1^2 + a2^2 + a3^2), where a1, a2, and a3 are the components of vector a. However, you didn't provide the components of vector a, so I cannot calculate its magnitude without that information.
The magnitude of vector b is |b| = √(b1^2 + b2^2 + b3^2), where b1, b2, and b3 are the components of vector b. You provided that a x b = (1, 2, 2), so |b| = √(1^2 + 2^2 + 2^2) = √(1 + 4 + 4) = √9 = 3.
Now, with the magnitude of vector b known (|b| = 3) and the dot product (a • b = √3), you can solve for the cosine of the angle θ:
√3 = |a| * 3 * cos(θ)
Now, divide both sides by (|a| * 3):
cos(θ) = √3 / (|a| * 3)
To find θ, take the arccosine (inverse cosine) of both sides:
θ = arccos(√3 / (|a| * 3))