Vector - practice problems - page 5 of 7
Number of problems found: 133
- Scalar product
Calculate the scalar product of two vectors: (2.5) (-1, -4) - Axial symmetry
Find the image A' of point A [1,2] in axial symmetry with the axis p: x = -1 + 3t, y = -2 + t (t = are a real number) - 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 then passing it ahead of it again 20 meters away. The car overtakes at a steady speed of 72 km/h, while the bus goes at a steady speed of 54 - Perpendicular direction
A speedboat moves relative to the water at a constant speed of 13 m/s. The speed of the water current in the river is 5 m/s a) At what angle concerning the water current must the boat sail to keep moving perpendicular to the banks of the river? b) At what - Boat in the lake A boatman walks along the ship's deck at a constant speed of 5 km/h in a direction that forms an angle of 60° with the direction of the ship's speed. The boat moves with respect to the lake's calm surface at a constant speed of 10 km/h. Determine graphica
- Rowboat River Current Speed
A rowboat sailing down a river covers a distance of 120 m downstream in 12 s and upstream in 24 s. Find the magnitude of the ship's velocity relative to the water and the current in the river. Both speeds are constant. - Ball Velocity Train Relative
We throw a ball in an express car traveling at a constant speed of 24 m/s, whose initial speed relative to the vehicle is 7 m/s. What is the initial velocity of the ball relative to the surface of the ground if we throw it a) in the direction of travel b) - 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 concerning the ground, b) the distance of his land from a - Calculate
Calculate the resulting speed of both vehicles after the collision of a car with a mass of m₁ = 1.5 tonnes travelling at 100 km/h and a truck with a mass of m₂ = 40 tonnes travelling at 90 km/h, if it is a head-on collision. Calculate the overload acting - Equation of the circle
Find the equation of the circle with the center at (1,20), which touches the line 8x+5y-19=0 - Two people
Two straight lines cross at right angles. Two people start simultaneously at the point of intersection. John walks at the rate of 4 kph on one road, and Jenelyn walks at the rate of 8 kph on the other road. How long will it take for them to be 20√5 km apa - Points collinear
Show that the point A(-1,3), B(3,2), C(11,0) are col-linear. - Clock angle
Calculate the magnitude of the angle formed by the lines p and q, which connect 1, 6 (line p), and 5, 8 (line q) on the clock face. - Angle between line and plane
Find the angle between the line given parametrically by x = 5 + t y = 1 + 3t z = -2t t ∈ R and the plane given by the equation 2x-y + 3z-4 = 0. - Three points 2
The three points are A(3, 8), B(6, 2), and C(10, 2). 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 = 580 N and F2 = 630 N, have an 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 (-1,-1) - Vector 7
Given vector OA(12,16) and vector OB(4,1). Find vector AB and vector |A|. - Forces on earth directions
A force of 60 N [North] and 80 N [East] is exerted on an object weight of 10 kg. What is the acceleration of the object?
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