Two separate cuboids with different orientation in space. Determine the angle between them, knowing the direction cosine matrix for each separate cuboid. u1=(0.62955056, 0.094432584, 0.77119944) u2=(0.14484653, 0.9208101, 0.36211633)
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 [-9; -2] B [2; 16] C [16; -2] and D [12; 18] 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.
Determine coordinates of the vector u=CD if C[19;-7], D[-16,-5].
- Coordinates of vector
Determine the coordinate of a vector u=CD if C(19;-7) and D(-16;-5)
- Linear independence
Determine if vectors u=(-4; -5) and v=(20; 25) are linear Linear dependent.
Determine the discriminant of the equation: ?
- Unit vector 2D
Determine coordinates of unit vector to vector AB if A[-6; 8], B[-18; 10].
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 = (-22, 11) and v = (16, 20)
- Vector sum
The magnitude of the vector u is 12 and the magnitude of the vector v is 8. Angle between vectors is 61°. What is the magnitude of the vector u + v?
- 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°
- Theorem prove
We want to prove the sentense: If the natural number n is divisible by six, then n is divisible by three. From what assumption we started?
- Scalar product
Calculate the scalar product of two vectors: (2.5) (-1, -4)
- Add vector
Given that P = (5, 8) and Q = (6, 9), find the component form and magnitude of vector PQ.
- Points collinear
Show that the point A(-1,3), B(3,2), C(11,0) are col-linear.
Line p passing through A[-10, 6] and has direction vector v=(3, 2). Is point B[7, 30] on the line p?
How much is sum of square root of six and the square root of 225?
- Six terms
Find the first six terms of the sequence a1 = -3, an = 2 * an-1