Vector - examples
Line p passing through A[-10, 1] and has direction vector v=(2, 4). Is point B[-20, -19] on the line p?
- Linear independence
Determine if vectors u=(3; -3) and v=(0; 3) are linear Linear dependent.
Determine coordinates of the vector u=CD if C[13;-8], D[-19,-13].
For vector w is true: w = 2u+2v. Determine coordinates of vector w if u=(-8, -5), v=(18, 19)
- Add vector
Given that P = (5, 8) and Q = (6, 9), find the component form and magnitude of vector PQ.
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?
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.
Calculate length of the vector v⃗ = (-2.5, 6.25, -4.25).
- Angle between vectors
Find the angle between the given vectors to the nearest tenth of a degree. u = (24, -1) and v = (12, 16)
- Airplane navigation
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)?
- Vector sum
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?
- Vector - basic operations
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
- Unit vector 2D
Determine coordinates of unit vector to vector AB if A[19; 10], B[-12; -6].
- Bearing - 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.
- Medians and sides
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.
- Two forces
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.
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)
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.
- Scalar 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°
- 3d vector component
The vector u = (3.9, u3) and the length of the vector u is 12. What is is u3?