Vector - examples

  1. Line
    img2 Line p passing through A[-10, 1] and has direction vector v=(2, 4). Is point B[-20, -19] on the line p?
  2. Linear independence
    colinear_vectors Determine if vectors u=(3; -3) and v=(0; 3) are linear Linear dependent.
  3. Vector
    vectors Determine coordinates of the vector u=CD if C[13;-8], D[-19,-13].
  4. Angle between vectors
    arccos Find the angle between the given vectors to the nearest tenth of a degree. u = (24, -1) and v = (12, 16)
  5. Vectors
    green For vector w is true: w = 2u+2v. Determine coordinates of vector w if u=(-8, -5), v=(18, 19)
  6. Add vector
    vectors_2 Given that P = (5, 8) and Q = (6, 9), find the component form and magnitude of vector PQ.
  7. Vectors
    vectors Vector a has coordinates (7; 16) and vector b has coordinates (15; -7). If the vector c = b - a, what is the magnitude of the vector c?
  8. Crossroads
    crossroad The rectangular crossroads comes passenger car and an ambulance, the ambulance left. Passenger car is at 45 km/h and ambulance 58 km/h. Calculate such a relative speed of the ambulance moves to the car.
  9. Vector
    some_vector Calculate length of the vector v⃗ = (-2.5, 6.25, -4.25).
  10. Airplane navigation
    triangle_airplane An airplane leaves an airport and flies due west 120 miles and then 150 miles in the direction S 23.32°W. How far is the plane from the airport (round to the nearest mile)?
  11. Vector sum
    vectors The magnitude of the vector u is 8 and the magnitude of the vector v is 11. Angle between vectors is 65°. What is the magnitude of the vector u + v?
  12. Vector - basic operations
    vectors_1 There are given points A [13; 11] B [23; -4] C [9; -1] and D [-11; 25] 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
  13. Unit vector 2D
    one_1 Determine coordinates of unit vector to vector AB if A[19; 10], B[-12; -6].
  14. 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.
  15. 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.
  16. Two forces
    vector-add Two forces with magnitudes of 25 and 30 pounds act on an object at angles of 10° and 100° respectively. Find the direction and magnitude of the resultant force. Round to two decimal places in all intermediate steps and in your final answer.
  17. 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=(0.62149553, 0.11709336, 0.77461762) u2=(0.046501848, 0.66652649, 0.74402958)
  18. Bearing
    compass A plane flew 50 km on a bearing 63°20' and the flew on a bearing 153°20' for 140km. Find the distance between the starting point and the ending point.
  19. 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°
  20. 3d vector component
    vectors_1 The vector u = (3.9, u3) and the length of the vector u is 12. What is is u3?

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