Sum of the two vectors - the result
Sum of vectors (size, magnitude) F = F1 + F2 = 39.051248379533
Directional angle of the resulting vector φ = 50°11'40″ = 50.194428907735° = 0.2788579 rad
F1=25 F2=30 α=90° x0=F1=25 y0=0 x1=F2 cosα=1.836970198721⋅10−15 y1=F2 sinα=30 x=x0+x1=25 y=y0+y1=30 F=x2+y2=39.051248379533 tanφ=y:x φ=arctany:x=50°11′40"=50.194428907735°=0.2788579 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.Analytically - by calculation, we calculate the sum of vectors most simply by dividing the vectors into x, y, or z components. We then add the individual vectors by components. We then calculate the size of the resulting vector from the Pythagorean theorem from its component form. We determine the direction vector trigonomically - by the arctangent of the y:x ratio.
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. - 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 lines
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. - Vector
Determine coordinates of the vector u=CD if C[12;-8], D[6,20]. - Points collinear
Show that the point A(-1,3), B(3,2), C(11,0) are col-linear. - 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) - 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. - 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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