# Vector + analytic geometry - problems

1. Triangle
Triangle KLM is given by plane coordinates of vertices: K[-12, -11] L[-15, -18] M[-13, -12]. Calculate its area and itsinterior angles.
2. Angle between vectors
Find the angle between the given vectors to the nearest tenth of a degree. u = (-22, 11) and v = (16, 20)
3. Line
Line p passing through A[-10, 6] and has direction vector v=(3, 2). Is point B[7, 30] on the line p?
4. Linear independence
Determine if vectors u=(-4; -5) and v=(20; 25) are linear Linear dependent.
5. Unit vector 2D
Determine coordinates of unit vector to vector AB if A[-6; 8], B[-18; 10].
6. 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?
7. 3d vector component
The vector u = (3.9, u3) and the length of the vector u is 12. What is is u3?
8. Vector
Determine coordinates of the vector u=CD if C[19;-7], D[-16,-5].
9. 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.
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.
11. 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.
12. Medians and sides
Triangle ABC in the plane Oxy; are the coordinates of the points: A = 2.7 B = -4.3 C-6-1 Try calculate lengths of all medians and all sides.
13. Resultant force
Calculate mathematically and graphically the resultant of a three forces with a common centre if: F1 = 50 kN α1 = 30° F2 = 40 kN α2 = 45° F3 = 40 kN α3 = 25°
14. Rectangle 39
Find the perimeter and area of the rectangular with vertices (-1, 4), (0,4), (0, -1), and (-4, 4)
15. Cuboids
Two separate cuboids with different orientation 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)
16. Two forces
The two forces F1 = 580N and F2 = 630N have the angle of 59 degrees. Calculate their resultant force F.
17. Find the 5
Find the equation with center at (1,20) which touches the line 8x+5y-19=0
18. Two people
Two straight lines cross at right angles. Two people start simultaneously at the point of intersection. John walking at the rate of 4 kph in one road, Jenelyn walking at the rate of 8 kph in the other road. How long will it take for them to be 20√5 km apar
19. Three points 2
The three points A(3, 8), B(6, 2) and C(10, 2). The point D is such that the line DA is perpendicular to AB and DC is parallel to AB. Calculate the coordinates of D.
20. Points collinear
Show that the point A(-1,3), B(3,2), C(11,0) are col-linear.

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For Basic calculations in analytic geometry is helpful line slope calculator. From coordinates of two points in the plane it calculate slope, normal and parametric line equation(s), slope, directional angle, direction vector, the length of segment, intersections the coordinate axes etc. Two vectors given by its magnitudes and by included angle can be added by our vector sum calculator.