Vector - math word problems

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?
Parallel and orthogonal
I need math help in this problem: a=(-5, 5 3) b=(-2,-4,-5) (they are vectors) Decompose the vector b into b=v+w where v is parallel to a and w is orthogonal to a, find v and w
Parametric form
Calculate the distance of point A [2,1] from the line p: X = -1 + 3 t Y = 5-4 t Line p has a parametric form of the line equation. ..
Find the 10
Find the value of t if 2tx+5y-6=0 and 5x-4y+8=0 are perpendicular, parallel, what angle does each of the lines make with the x-axis, find the angle between the lines?
Coordinates of square vertices
The ABCD square has the center S [−3, −2] and the vertex A [1, −3]. Find the coordinates of the other vertices of the square.
Scalar product
Calculate the scalar product of two vectors: (2.5) (-1, -4)
Coordinates of vector
Determine the coordinate of a vector u=CD if C(19;-7) and D(-16;-5)
Overtaking
On the direct road, the passenger car overtakes the slower bus by starting to overtake 20 meters from the bus and after passing it ahead of it again 20 meters away. The car overtakes at a steady speed of 72 km/h, the bus goes at a steady speed of 54 km/h.
Paratrooper
After the parachute is opened, the paratrooper drops to the ground at a constant speed of 2 m/s, with the sidewinding at a steady speed of 1.5 m/s. Find: a) the magnitude of its resulting velocity with respect to the ground, b) the distance of his land f
Find the 5
Find the equation with center at (1,20) which touches the line 8x+5y-19=0
Points collinear
Show that the point A(-1,3), B(3,2), C(11,0) are col-linear.
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 on the other road. How long will it take for them to be 20√5 km apa
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.
Two forces
The two forces F1 = 580N and F2 = 630N have the angle of 59 degrees. Calculate their resultant force F.
Rectangle 39
Find the perimeter and area of the rectangular with vertices (-1, 4), (0,4), (0, -1), and (-4, 4)
Vector 7
Given vector OA(12,16) and vector OB(4,1). Find vector AB and vector |A|.