Vector - math problems
Number of problems found: 64
- CoG center
Find the position of the center of gravity of a system of four mass points having masses, m1, m2 = 2 m1, m3 = 3 m1, and m4 = 4 m1, if they lie at the vertices of an isosceles tetrahedron. (in all cases, between adjacent material points, the distance
- The bomber
From what distance in front of the target must a parachute load be dropped from an aircraft flying at an altitude of 1260 m if it slopes at a speed of 5.6 m/s and at the same time is carried in the direction of movement at a speed of 12 m/s. What is the d
- Space vectors 3D
The vectors u = (1; 3; -4), v = (0; 1; 1) are given. Find the size of these vectors, calculate the angle of the vectors, the distance between the vectors.
- Mass point
Two equal forces of 30 Newtons act on a mass point. Find the magnitude of the resultant force if these forces form an angle of 42°.
- Proportional relationship
The ordered pairs (6,24) and (1, s) represent a proportional relationship. Find the value of s.
- Vectors abs sum diff
The vectors a = (4,2), b = (- 2,1) are given. Calculate: a) |a+b|, b) |a|+|b|, c) |a-b|, d) |a|-|b|.
- Perpendicular projection
Determine the distance of a point B[1, -3] from the perpendicular projection of a point A[3, -2] on a straight line 2 x + y + 1 = 0.
- Place vector
Place the vector AB, if A (3, -1), B (5,3) in the point C (1,3) so that AB = CO
- Ascend vs. descent
Which function is growing? a) y = 2-x b) y = 20 c) y = (x + 2). (-5) d) y = x-2
- Three points
Three points K (-3; 2), L (-1; 4), M (3, -4) are given. Find out: (a) whether the triangle KLM is right b) calculate the length of the line to the k side c) write the coordinates of the vector LM d) write the directional form of the KM side e) write the d
- Vector v4
Find the vector v4 perpendicular to vectors v1 = (1, 1, 1, -1), v2 = (1, 1, -1, 1) and v3 = (0, 0, 1, 1)
- Calculate 6
Calculate the distance of a point A[0, 2] from a line passing through points B[9, 5] and C[1, -1].
Calculate the size of the smaller of the angles determined by lines A1 A4 and A2 A10 in the regular dodecagon A1A2A3. .. A12. Express the result in degrees.
- The modulus
Find the modulus of the complex number 2 + 5i
- Decide 2
Decide whether points A[-2, -5], B[4, 3] and C[16, -1] lie on the same line
- Vector perpendicular
Find the vector a = (2, y, z) so that a⊥ b and a ⊥ c where b = (-1, 4, 2) and c = (3, -3, -1)
- Vector equation
Let’s v = (1, 2, 1), u = (0, -1, 3) and w = (1, 0, 7) . Solve the vector equation c1 v + c2 u + c3 w = 0 for variables c1 c2, c3 and decide weather v, u and w are linear dependent or independent
- Angle of the body diagonals
Using vector dot product calculate the angle of the body diagonals of the cube.
- Coordinates of a centroind
Let’s A = [3, 2, 0], B = [1, -2, 4] and C = [1, 1, 1] be 3 points in space. Calculate the coordinates of the centroid of △ABC (the intersection of the medians).
- Angled cyclist turn
The cyclist passes through a curve with a radius of 20 m at 25 km/h. How much angle does it have to bend from the vertical inward to the turn?
Our vector sum calculator can add two vectors given by their magnitudes and by included angle.