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)

Correct answer:

a =  62.7801 °

Step-by-step explanation:

s=0.62955056 0.14484653+0.094432584 0.9208101+0.77119944 0.362116330.4574 a=180πarccos(s)=180πarccos(0.4574)=62.7801=624648"



We will be pleased if You send us any improvements to this math problem. Thank you!



Showing 1 comment:
#
Matikar
use scalar products to determine angle between two 3D vectors (if direction cosines gives -> its unit vectors)

avatar






Tips to related online calculators
Line slope calculator is helpful for basic calculations in analytic geometry. The coordinates of two points in the plane calculate slope, normal and parametric line equation(s), slope, directional angle, direction vector, the length of the segment, intersections of the coordinate axes, etc.
Our vector sum calculator can add two vectors given by their magnitudes and by included angle.
Most natural application of trigonometry and trigonometric functions is a calculation of the triangles. Common and less common calculations of different types of triangles offers our triangle calculator. Word trigonometry comes from Greek and literally means triangle calculation.

Related math problems and questions:

  • Space vectors 3D
    vectors The vectors u = (1; 3; -4), v = (0; 1; 1) are given. Find the size of these vectors, calculate the angle of the vectors, the distance between the vectors.
  • Angle between vectors
    arccos Find the angle between the given vectors to the nearest tenth of a degree. u = (-22, 11) and v = (16, 20)
  • Angle of the body diagonals
    body_diagonals_angle Using vector dot product calculate the angle of the body diagonals of the cube.
  • Vector sum
    vectors 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
    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°
  • Triangle
    sedlo Plane coordinates of vertices: K[11, -10] L[10, 12] M[1, 3] give Triangle KLM. Calculate its area and its interior angles.
  • Vector v4
    scalar_product Find the vector v4 perpendicular to vectors v1 = (1, 1, 1, -1), v2 = (1, 1, -1, 1) and v3 = (0, 0, 1, 1)
  • Three vectors
    vectors_sum0 The three forces whose amplitudes are in ratio 9:10:17 act in the plane at one point to balance. Determine the angles of each two forces.
  • Scalar product
    vectors_sum0_2 Calculate the scalar product of two vectors: (2.5) (-1, -4)
  • Find the 10
    lines Find the value of t if 2tx+5y-6=0 and 5x-4y+8=0 are perpendicular, parallel, what angle does each of the lines make with the x-axis, find the angle between the lines?
  • Vector - basic operations
    vectors_1 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
  • Decide 2
    vectors2 Decide whether points A[-2, -5], B[4, 3] and C[16, -1] lie on the same line
  • Forces
    ijk In point O acts three orthogonal forces: F1 = 20 N, F2 = 7 N, and F3 = 19 N. Determine the resultant of F and the angles between F and forces F1, F2, and F3.
  • Vector perpendicular
    3dperpendicular Find the vector a = (2, y, z) so that a⊥ b and a ⊥ c where b = (-1, 4, 2) and c = (3, -3, -1)
  • Diagonal
    krychle Determine the dimensions of the cuboid, if diagonal long 53 dm has an angle with one edge 42° and with another edge 64°.
  • The angle of view
    pole_1 Determine the angle of view at which the observer sees a rod 16 m long when it is 18 m from one end and 27 m from the other.
  • Parallel and orthogonal
    vectors2 I need math help in this problem: a=(-5, 5 3) b=(-2,-4,-5) (they are vectors) Decompose the vector b into b=v+w where v is parallel to a and w is orthogonal to a, find v and w