# Vector - examples

- Points collinear

Show that the point A(-1,3), B(3,2), C(11,0) are col-linear. - Triangle

Triangle KLM is given by plane coordinates of vertices: K[-4, -18] L[-13, 15] M[-1, 8]. Calculate its area and itsinterior angles. - Crossroads

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)? - Vector

Calculate length of the vector v⃗ = (9.75, 6.75, -6.5, -3.75, 2). - Line

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]. - Vectors

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? - 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? - 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? - Vector

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. - Vectors

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. - 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° - 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.

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Two vectors given by its magnitudes and by included angle can be added by our vector sum calculator.