Vector - practice problems - page 6 of 7
Number of problems found: 127
- Vector magnitudes
Determine the size of the vectors u = (2,4) and v = (-3,3) - Parametric equations
Write the parametric equations of height hc in triangle ABC: A = [5; 6], B = [- 2; 4], C = [6; -1] - Distance of the parallels
Find the distance of the parallels, which equations are: x = 3-4t, y = 2 + t and x = -4t, y = 1 + t (instructions: select a point on one line and find its distance from the other line) - Acting
Two locomotives are involved in a train set. One locomotive pulls the train, and the other pushes it. The pulling locomotive exerts a force of 500 kN on the train, and the pushing locomotive exerts a force of 400 kN. a) Draw a diagram of the described sit - Line equation
The given triangle is ABC: A [-3; -1] B [5; 3] C [1; 5] Write the line equation that passes through the vertex C parallel to the side AB. - Vector triangle
Calculate the interior angles of triangle ABC using vectors. Coordinates A [2; 4] B [4; 6] C [0; -4]. Calculate directional vectors of sides, parametric and general equations of sides, parametric and general equations of lines, calculate area, calculate h - Journey
Charles and Eva stand in front of his house. Charles went to school south at a speed of 5.4 km/h, and Eva went to the store on a bicycle eastwards at 21.6 km/h. How far apart are they after 10 minutes? - Scalar dot product
Calculate u.v if |u| = 5, |v| = 2 and when the angle between the vectors u, v is: a) 60° b) 45° c) 120° - Ballistic curve
The soldier fired the ballistic grenade at a 45° angle. The first half ascended, and the second fell. How far and height did it reach if his average speed was 1200 km/h, and what 12 seconds were taken from the shot to impact? - Airplane navigation
An airplane leaves an airport and flies west 120 miles and then 150 miles in the direction S 35.95°W. How far is the plane from the airport (round to the nearest mile)? - Two forces
Two forces with magnitudes of 25 and 30 pounds act on an object at 10° and 100° angles. Find the direction and magnitude of the resultant force. Round to two decimal places in all intermediate steps and your final answer. - Add vector
Given that P = (5, 8) and Q = (6, 9), find the component form and magnitude of vector PQ. - 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 - 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 the difference of vectors u-v d. Determine the coordinates of the vecto
- 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 2 and the magnitude of the vector v is 11. The angle between vectors is 64°. What is the magnitude of the vector u + v?
- Angle between vectors
Find the angle between the given vectors to the nearest tenth degree. u = (-1, 24) and v = (-8, -21) - Linear independence
Determine if vectors u=(-4; -10) and v=(-2; -7) are linear dependents. - Unit vector 2D
Find coordinates of unit vector to vector AB if A[-6; 8], B[-18; 10].
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