Analytic geometry + vector - practice problems - last page
Number of problems found: 58
- Cuboids
Two separate cuboids with different orientations are in space. Determine the angle between them, knowing the direction cosine matrix for each separate cuboid. u1=(0.62955056, 0.094432584, 0.77119944) u2=(0.14484653, 0.9208101, 0.36211633) - Medians and sides
Triangle ABC in the plane Oxy has the coordinates of the points: A = 2.7 B = -4.3 C-6-1 Try to calculate the lengths of all medians and all sides. - 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 of the 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) - 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. - 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 Given points A[-9; -2], B[2; 16], C[16; -2], and D[12; 18]: a. Determine the coordinates of vectors u = AB, v = CD, and s = DB. b. Calculate the sum of vectors u + v. c. Calculate the difference of vectors u − v. d. Determine the coordinates of the vector
- 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[3; 6], B[15; -8]. - Vector Determine coordinates of the vector u=CD if C[12;-8], D[6,20].
- Triangle
Plane coordinates of vertices: K[9, 5] L[-4, 8] M[3, 20] give Triangle KLM. Calculate its area and its interior angles. - Line
Line p passes through A[5, -3] and has a direction vector v=(2, 3). Is point B[3, -6] on the line p? - Square
Points A[9,9] and B[-4,1] are adjacent vertices of square ABCD. Calculate the area of square ABCD.
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