Sum of the two vectors - the result
Sum of vectors (size, magnitude) F = F1 + F2 = 1053.4181625282
Directional angle of the resulting vector φ = 30°50'21″ = 30.839276373726° = 0.1713293 rad
F1=580 F2=630 α=59° x0=F1=580 y0=0 x1=F2 cosα=324.47398719333 y1=F2 sinα=540.01539944233 x=x0+x1=904.47398719333 y=y0+y1=540.01539944233 F=x2+y2=1053.4181625282 tanφ=y:x φ=arctany:x=30°50′21"=30.839276373726°=0.1713293 rad
How to add two vectors
If we place the vectors at one starting point, the vectors form two sides of the parallelogram. By completing the remaining two parallel sides, we create a parallelogram. The resulting vector of the sum is the oriented diagonal of this parallelogram starting at the location point of the vectors.Analyticky - výpočtem vypočítáme součet vektorů nejjednodušeji tak, že vektory rozložíme do složek x, y, případně z. Jednotlivé vektory pak sečteme po složkách. Velikost výsledného vektoru pak dopočítáme z Pythagorovy věty z jeho složkového tvaru. Směrový vektor určíme trigonometricky - arkustangensem poměru y:x.
Vectors in word problems
- 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 - Coordinates of vector
Determine the coordinate of a vector u=CD if C(19;-7) and D(-16;-5) - Place vector
Place the vector AB if A (3, -1), B (5,3) in point C (1,3) so that AB = CO. - Vector
Determine coordinates of the vector u=CD if C[12;-8], D[6,20].
- 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? - Perpendicular 28823
Points A(1,2), B(4,-2) and C(3,-2) are given. Find the parametric equations of the line that: a) It passes through point C and is parallel to the line AB, b) It passes through point C and is perpendicular to line AB. - 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) - Points collinear
Show that the point A(-1,3), B(3,2), C(11,0) are col-linear. - 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 - 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). - Ascend vs. descent
Which function is growing? a) y = 2-x b) y = 20 c) y = (x + 2). (-5) d) y = x-2 - Vector v4
Find the vector v4 perpendicular to the vectors v1 = (1, 1, 1, -1), v2 = (1, 1, -1, 1) and v3 = (0, 0, 1, 1) - Linear independence
Determine if vectors u=(-4; -10) and v=(-2; -7) are linear dependents.
Write the parametric equations of height hc in triangle ABC: A = [5; 6], B = [- 2; 4], C = [6; -1]more math problems »