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 result:

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


a=(5,5,3) b=(2,4,5)  b=v+w va=>v=ka  wa=>w.a=0   2=v1+w1 4=v2+w2 5=v3+w3 v1=5 k=2.1186 v2=5 k v3=3 k w1 (5)+w2 5+w3 3=0  v1+w1=2 v2+w2=4 v3+w3=5 5k+v1=0 5kv2=0 3kv3=0 5w15w23w3=0  k=25590.423729 v1=125592.118644 v2=125592.118644 v3=75591.271186 w1=243594.118644 w2=111591.881356 w3=220593.728814

We would be pleased if you find an error in the word problem, spelling mistakes, or inaccuracies and send it to us. Thank you!

Showing 0 comments:

Tips to related online calculators
Our vector sum calculator can add two vectors given by its 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:

Next similar math problems:

  • 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_2 Calculate the scalar product of two vectors: (2.5) (-1, -4)
  • 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?
  • 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_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
  • Faces diagonals
    cuboid_1 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
  • Angle of the body diagonals
    body_diagonals_angle Using vector dot product calculate the angle of the body diagonals of the cube.
  • 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°
  • 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
  • Coordinates of square vertices
    ctverec_2 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.
  • Vectors
    green For vector w is true: w = 2u-5v. Determine coordinates of vector w if u=(3, -1), v=(12, -10)
  • 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?