Vector - practice problems - page 4 of 7
Directions: Provide a careful solution to each problem, showing all steps in your work.Number of problems found: 133
- Motorcyclist and a car
The passenger car left at 7:00 and was heading east at a speed of 60 km/h. A motorcyclist left the same place and headed north at 40 km/h. What will be their air distance at ten o'clock? - Aircraft climbing
The average climb angle of the aircraft is 11° 20', and its average speed is 400 km/h. How long does it take to climb to a height of 3000 m? - 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 whether v, u, and w are linear dependent or independent - Angle of the body diagonals
Using the vector dot product calculate the angle of the body diagonals of the cube. - Coordinates of a centroind
Let 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. - Military distance deviation A military unit marches in a northerly direction from point A to point B, 15 km away. From place B, it goes 12 km in a northeasterly direction to place C. Determine the direct distance of cities A and C and certainly the deviation -alpha- by which the uni
- Perpendicular and parallel
Find the value of t if 2tx+5y-6=0 and 5x-4y+8=0 are perpendicular and parallel lines. What angle does each line make with the x-axis, and find the angle between the lines? - Position vector of a point mass
The position vector of a point mass moving in a plane can be expressed in the established reference frame by the relation: r(t) = (t²+ 2t + 1 ; 2t + 1), where t is time in seconds and the vector coordinates are in meters. Calculate: a) What is the positio - Position vector
The position vector of a point mass moving in a plane can be expressed in the established reference frame by the relation: r(t) = (1 + 5t + 2t² ; 3t + 1), where t is time in seconds and the vector coordinates are in meters. Calculate: a) What is the posit - Vectors 5 The position vector of a material point moving in a plane can be expressed in the introduced reference frame by the relation: r(t) = (2t + 3t²; 6t + 3), where t is time in seconds and the coordinates of the vector are in metres. Calculate: a) what is the
- Position vector of a point mass
The position vector of a point mass moving in a plane can be expressed in the established reference frame by the relation: r(t) = (6t²+ 4t ; 3t + 1) where t is time in seconds and the vector coordinates are in meters. Calculate: a) What is the position of - Raindrops
The train is moving at a speed of 60 km/h. Raindrops falling vertically in the absence of wind (with uniform movement due to the action of air resistance) leave traces on the windows of the train, deviating from the vertical direction by 30°. How fast are - Direction Vectors Points
A (5; -4) B (1; 3) C (-2; 0) D (6; 2) Calculate the direction vector a) a = AB b) b = BC c) c = CD - 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.
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