Parallel and orthogonal

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

Correct answer:

v1 =  2.1186
v2 =  -2.1186
v3 =  -1.2712
w1 =  -4.1186
w2 =  -1.8814
w3 =  -3.7288

Step-by-step explanation:

v2=(2.1186)=2.1186
v3=(1.2712)=1.2712
w1=(4.1186)=4.1186
w2=(1.8814)=1.8814
w3=(3.7288)=3.7288



Did you find an error or inaccuracy? Feel free to write us. Thank you!



avatar




Tips to related online calculators
Our vector sum calculator can add two vectors given by their magnitudes and by included angle.
Do you have a system of equations and looking for calculator system of linear equations?

You need to know the following knowledge to solve this word math problem:

Related math problems and questions:

  • 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)
  • Scalar product
    vectors_sum0 Calculate the scalar product of two vectors: (2.5) (-1, -4)
  • 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.
  • 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)
  • 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)
  • Three points 2
    vectors_sum0 The three points A(3, 8), B(6, 2) and C(10, 2). The point D is such that the line DA is perpendicular to AB, and DC is parallel to AB. Calculate the coordinates of D.
  • 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?
  • 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°
  • Vector equation
    collinear2 Let’s v = (1, 2, 1), u = (0, -1, 3) and w = (1, 0, 7) . Solve the vector equation c1 v + c2 u + c3 w = 0 for variables c1 c2, c3 and decide weather v, u and w are linear dependent or independent
  • Cuboids
    3dvectors 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)
  • Vector - basic operations
    vectors 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
  • Angle of the body diagonals
    body_diagonals_angle Using vector dot product calculate the angle of the body diagonals of the cube.
  • Faces diagonals
    cuboid If a cuboid's diagonals are x, y, and z (wall diagonals or three faces), then find the cuboid volume. Solve for x=1.3, y=1, z=1.2
  • Vectors
    vectors Vector a has coordinates (8; 10) and vector b has coordinates (0; 17). If the vector c = b - a, what is the magnitude of the vector c?
  • Find the 5
    distance-between-point-line Find the equation of the circle with center at (1,20), which touches the line 8x+5y-19=0
  • Vectors
    green For vector w is true: w = 2u-5v. Determine coordinates of vector w if u=(3, -1), v=(12, -10)
  • Coordinates of square vertices
    ctverec The ABCD square has the center S [−3, −2] and the vertex A [1, −3]. Find the coordinates of the other vertices of the square.