# Sum of the two vectors

### 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

- Coordinates of vector

Determine the coordinate of a vector u=CD if C(19;-7) and D(-16;-5) - 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 - 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 - Linear independence

Determine if vectors u=(-4; -10) and v=(-2; -7) are linear dependents. - Parametric equations

Write the parametric equations of height hc in triangle ABC: A = [5; 6], B = [- 2; 4], C = [6; -1] - 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)

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