# Vector - examples

- Triangle

Triangle KLM is given by plane coordinates of vertices: K[-19, -8] L[8, -12] M[2, -6]. Calculate its area and itsinterior angles. - Crossroads

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. - Angle between vectors

Find the angle between the given vectors to the nearest tenth of a degree. u = (24, -1) and v = (12, 16) - Vector

Calculate length of the vector v⃗ = (-2.5, 6.25, -4.25). - 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 23.32°W. How far is the plane from the airport (round to the nearest mile)? - Linear independence

Determine if vectors u=(3; -3) and v=(0; 3) are linear Linear dependent. - Line

Line p passing through A[-10, 1] and has direction vector v=(2, 4). Is point B[-20, -19] on the line p? - Unit vector 2D

Determine coordinates of unit vector to vector AB if A[19; 10], B[-12; -6]. - 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? - 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? - 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. - Vector

Determine coordinates of the vector u=CD if C[13;-8], D[-19,-13]. - 3d vector component

The vector u = (3.9, u3) and the length of the vector u is 12. What is is u3? - Vectors

For vector w is true: w = 2u+2v. Determine coordinates of vector w if u=(-8, -5), v=(18, 19) - 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° - 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 - Bearing

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. - 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. - Add vector

Given that P = (5, 8) and Q = (6, 9), find the component form and magnitude of vector PQ.

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