Vector - examples
Triangle KLM is given by plane coordinates of vertices: K[-12, -11] L[-15, -18] M[-13, -12]. Calculate its area and itsinterior angles.
The rectangular crossroads comes passenger car and an ambulance, the ambulance left. Passenger car is at 43 km/h and ambulance 52 km/h. Calculate such a relative speed of the ambulance moves to the car.
- Angle between vectors
Find the angle between the given vectors to the nearest tenth of a degree. u = (-22, 11) and v = (16, 20)
- 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.
- Airplane navigation
An airplane leaves an airport and flies due west 120 miles and then 150 miles in the direction S 44.1°W. How far is the plane from the airport (round to the nearest mile)?
Calculate length of the vector v⃗ = (9.75, 6.75, -6.5, -3.75, 2).
Line p passing through A[-10, 6] and has direction vector v=(3, 2). Is point B[7, 30] on the line p?
- Linear independence
Determine if vectors u=(-4; -5) and v=(20; 25) are linear Linear dependent.
- Unit vector 2D
Determine coordinates of unit vector to vector AB if A[-6; 8], B[-18; 10].
- 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?
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?
- 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.
- 3d vector component
The vector u = (3.9, u3) and the length of the vector u is 12. What is is u3?
Determine coordinates of the vector u=CD if C[19;-7], D[-16,-5].
- Three vectors
The three forces whose amplitudes are in ratio 9:10:17 act in the plane at one point so that they are in balance. Determine the angles of the each two forces.
For vector w is true: w = 2u-5v. Determine coordinates of vector w if u=(3, -1), v=(12, -10)
- Vector - basic operations
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.
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°
- 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 vectors given by its magnitudes and by included angle can be added by our vector sum calculator.