Analytic geometry + vector - practice problems - last page
Number of problems found: 56
- Resultant force
Calculate mathematically and graphically the resultant of three forces with a common center if: F1 = 50 kN α1 = 30° F2 = 40 kN α2 = 45° F3 = 40 kN α3 = 25° - Three vectors
The three forces whose amplitudes are in ratio 9:10:17 act in the plane at one point to balance. Determine the angles of each two forces. - 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)
- Equation 2604
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. - Add vector
Given that P = (5, 8) and Q = (6, 9), find the component form and magnitude of vector PQ. - 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 - Vector sum
The magnitude of the vector u is 12 and the magnitude of the vector v is 8. The angle between vectors is 61°. 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 = (6, 22) and v = (10, -11) - 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]. - Vector
Determine coordinates of the vector u=CD if C[12;-8], D[6,20]. - Triangle
Plane coordinates of vertices: K[19, -4] L[9, 13] M[-20, 8] give Triangle KLM. Calculate its area and its interior angles.
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