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?

Result

x =  17.35

Solution:

u+v2=u2+v22uvcos(18061) u+v=17.35|u+v|^2 = |u|^2+|v|^2-2|u||v|\cos (180 ^\circ -61 ^\circ ) \ \\ |u+v| = 17.35



Our examples were largely sent or created by pupils and students themselves. Therefore, we would be pleased if you could send us any errors you found, spelling mistakes, or rephasing the example. Thank you!





Leave us a comment of this math problem and its solution (i.e. if it is still somewhat unclear...):

Showing 0 comments:
1st comment
Be the first to comment!
avatar




Tips to related online calculators
For Basic calculations in analytic geometry is helpful line slope calculator. From coordinates of two points in the plane it calculate slope, normal and parametric line equation(s), slope, directional angle, direction vector, the length of segment, intersections the coordinate axes etc.
Two vectors given by its magnitudes and by included angle can be added by our vector sum calculator.
Cosine rule uses trigonometric SAS triangle calculator.
See also our trigonometric triangle calculator.

Following knowledge from mathematics are needed to solve this word math problem:

Next similar math problems:

  1. Add vector
    vectors_2 Given that P = (5, 8) and Q = (6, 9), find the component form and magnitude of vector PQ.
  2. 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°
  3. 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)
  4. Bearing - navigation
    navigation A ship travels 84 km on a bearing of 17°, and then travels on a bearing of 107° for 135 km. Find the distance of the end of the trip from the starting point, to the nearest kilometer.
  5. 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.
  6. Vector
    vectors Determine coordinates of the vector u=CD if C[19;-7], D[-16,-5].
  7. Coordinates of vector
    vectors_2 Determine the coordinate of a vector u=CD if C(19;-7) and D(-16;-5)
  8. Coordinates of a centroind
    triangle_234 Let’s A = [3, 2, 0], B = [1, -2, 4] and C = [1, 1, 1] be 3 points in space. Calculate the coordinates of the centroid of △ABC (the intersection of the medians).
  9. Line
    img2 Line p passing through A[-10, 6] and has direction vector v=(3, 2). Is point B[7, 30] on the line p?
  10. Points collinear
    collinear Show that the point A(-1,3), B(3,2), C(11,0) are col-linear.
  11. Medians and sides
    taznice3 Triangle ABC in the plane Oxy; are the coordinates of the points: A = 2.7 B = -4.3 C-6-1 Try calculate lengths of all medians and all sides.
  12. Greatest angle
    triangles_4 Calculate the greatest triangle angle with sides 197, 208, 299.
  13. Side c
    trig-cos-law In △ABC a=2, b=4 and ∠C=100°. Calculate length of the side c.
  14. Scalene triangle
    triangles_1 Solve the triangle: A = 50°, b = 13, c = 6
  15. Theorem prove
    thales_1 We want to prove the sentence: If the natural number n is divisible by six, then n is divisible by three. From what assumption we started?
  16. Laws
    pyt_triangle From which law follows directly the validity of Pythagoras' theorem in the right triangle? ?
  17. Center
    triangle_axis Calculate the coordinates of the center of gravity T [x, y] of triangle ABC; A[11,4] B[13,-7] C[-17,-18].