# Cuboids

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)

**Result****Leave us a comment of example and its solution (i.e. if it is still somewhat unclear...):**

**Showing 1 comment:**

**Matikar**

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:

- Geometric progression 2

There is geometric sequence with a_{1}=5.7 and quotient q=-2.5. Calculate a_{17}. - Median and modus

Radka made 50 throws with a dice. The table saw fit individual dice's wall frequency: Wall Number: 1 2 3 4 5 6 frequency: 8 7 5 11 6 13 Calculate the modus and median of the wall numbers that Radka fell. - 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. - Coordinates of vector

Determine the coordinate of a vector u=CD if C(19;-7) and D(-16;-5) - Vector

Determine coordinates of the vector u=CD if C[19;-7], D[-16,-5]. - Unit vector 2D

Determine coordinates of unit vector to vector AB if A[-6; 8], B[-18; 10]. - Vectors

For vector w is true: w = 2u-5v. Determine coordinates of vector w if u=(3, -1), v=(12, -10) - 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? - Add vector

Given that P = (5, 8) and Q = (6, 9), find the component form and magnitude of vector PQ. - Line

Line p passing through A[-10, 6] and has direction vector v=(3, 2). Is point B[7, 30] on the line p? - Points collinear

Show that the point A(-1,3), B(3,2), C(11,0) are col-linear. - The confectionery

The confectionery sold 5 kinds of ice cream. In how many ways can I buy 3 kinds if order of ice creams does not matter? - Sequence

Between numbers 1 and 53 insert n members of the arithmetic sequence that its sum is 702. - Six terms

Find the first six terms of the sequence a1 = -3, an = 2 * an-1