The angle between two vectors can be calculated using the dot product formula:
cos(theta) = (A dot B) / (|A| * |B|),
where A and B are the vectors, dot represents the dot product, |A| represents the magnitude of vector A, and theta represents the angle between the vectors.
In this case, we have two vectors:
A = iCAP + jCAP + kCAP B = iCAP
To find the angle between A and B, we need to calculate the dot product of A and B, as well as their magnitudes.
Dot product (A dot B) = (iCAP + jCAP + kCAP) dot (iCAP) = (1 * 1) + (0 * 0) + (0 * 0) = 1
Magnitude of A = |A| = sqrt((1^2) + (1^2) + (1^2)) = sqrt(3)
Magnitude of B = |B| = sqrt((1^2) + (0^2) + (0^2)) = sqrt(1) = 1
Now we can calculate the angle using the formula:
cos(theta) = (A dot B) / (|A| * |B|) theta = acos((A dot B) / (|A| * |B|))
theta = acos(1 / (sqrt(3) * 1)) theta = acos(1 / sqrt(3)) theta ≈ 54.74 degrees
Therefore, the angle between iCAP + jCAP + kCAP and iCAP is approximately 54.74 degrees.