Two separate cuboids with different orientation in space. Determine the angle between them, knowing the direction cosine matrix for each separate cuboid. u1=(0.62149553, 0.11709336, 0.77461762) u2=(0.046501848, 0.66652649, 0.74402958)
Leave us a comment of example and its solution (i.e. if it is still somewhat unclear...):
Showing 1 comment:
use scalar products to determine angle between two 3D vectors (if direction cosines gives -> its unit vectors)
To solve this example are needed these knowledge from mathematics:
Next similar examples:
- Vector - basic operations
There are given points A [13; 11] B [23; -4] C [9; -1] and D [-11; 25] a. Determine the coordinates of the vectors u=AB v=CD s=DB b. Calculate the sum of the vectors u + v c. Calculate difference of vectors u-v d. Determine the coordinates of the vector w
- AS sequence
In an arithmetic sequence is given the difference d = -2 and a78 = 518. a) Determine the value of a67 b) Determine the sum of 78 members.
Determine coordinates of the vector u=CD if C[13;-8], D[-19,-13].
- Unit vector 2D
Determine coordinates of unit vector to vector AB if A[19; 10], B[-12; -6].
For vector w is true: w = 2u+2v. Determine coordinates of vector w if u=(-8, -5), v=(18, 19)
Determine the discriminant of the equation: ?
Determine the quadratic equation absolute coefficient q, that the equation has a real double root and the root x calculate: ?
- Angle between vectors
Find the angle between the given vectors to the nearest tenth of a degree. u = (24, -1) and v = (12, 16)
- Scalar dot product
Calculate u.v if |u| = 5, |v| = 2 and when angle between the vectors u, v is: a) 60° b) 45° c) 120°
- Vector sum
The magnitude of the vector u is 8 and the magnitude of the vector v is 11. Angle between vectors is 65°. What is the magnitude of the vector u + v?
Between numbers 2 and 78 insert n members of the arithmetic sequence that its sum is 600.
Line p passing through A[-10, 1] and has direction vector v=(2, 4). Is point B[-20, -19] on the line p?
- Add vector
Given that P = (5, 8) and Q = (6, 9), find the component form and magnitude of vector PQ.
How much is sum of square root of six and the square root of 441?
- Sequence 3
Write the first 5 members of an arithmetic sequence: a7=-51, a17=-121.