6/14/2023 0 Comments Parallel vectors![]() ![]() Vector: Displacement as -4 ft, velocity -40 mph indicate the direction. Scalar: Speed as 40 mph, Time as 4 hours which do not indicate any direction which indicate the direction of the quantity and its magnitude. Common examples of vectors are displacement, velocity, acceleration, force, etc. These are real values accompanied by their units of measurements. The common examples of scalars are distance, speed, time, etc. The only difference between scalars and vectors is that a scalar is a quantity that does not depend on direction whereas a vector is a physical quantity that has magnitude as well as direction. A vector is defined by its magnitude and direction, regardless of where its initial point is located. We explore this idea in more detail later in the chapter. Two vectors are said to be parallel if they have the same or opposite directions. A closely related concept is the idea of parallel vectors. Basic operations of addition, subtraction, and multiplication are applicable on both scalars and vectors. Each arrow has the same length and direction. On the other hand, vectors are physical quantities that have magnitudes as well as directions. Scalars are nothing but real numbers, sometimes accompanied by unit measurements. Physical quantities that do not have any direction are called scalars. Vectors are usually represented in bold lowercase such as a or using an arrow over the letter as \(\vec\) For example, velocity, displacement, acceleration, force are all vector quantities that have a magnitude as well as a direction. ![]() Vectors play an important role in physics. We will study the operations on vectors in detail in this article. Various operations can be applied to vectors such as addition, subtraction, and multiplication. ![]() Vectors have an initial point at the point where they start and a terminal point that tells the final position of the point. Vectors in math is a geometric entity that has both magnitude and direction. Vectors in Euclidean Geometry- Definition Vectors have many applications in maths, physics, engineering, and various other fields. Vectors are also called Euclidean vectors or Spatial vectors. The length of the line between the two points A and B is called the magnitude of the vector and the direction of the displacement of point A to point B is called the direction of the vector AB. The handle of the wagon makes an angle of 30 o with the ground.A vector is a Latin word that means carrier. Hence, in the given figure, the following vectors are collinear:, , and. Collinear vectors are two or more vectors parallel to the same line irrespective of their magnitudes and direction. Anne pulls a wagon on a horizontal surface with a force of 50 pounds. In the figure given below, identify Collinear, Equal and Coinitial vectors: Solution: By definition, we know that.What is the magnitude of the effective force pulling the box up the plane? The inclined plane makes a 25 o angle with the horizontal. A 22 pound force that makes an angle of 12 o with an inclined plane is pulling a box up the plane.The inclined plane makes a 20 o angle with the horizontal. A 30 pound force that makes an angle of 32 o with an inclined plane is pulling a box up the plane.Find the magnitude of the force required to keep the car from rolling down the hill. A 1900 pound car is parked on a street that makes an angle of 10 o with the horizontal.A 1780 pound car is parked on a street that makes an angle of 15 o with the horizontal.What is the magnitude of the force required for Sam to keep Sarah from sliding down the hill. The weight of Sarah and the sled is 125 pounds. Sarah is on a sled on the side of a hill inclined at 60 o.What is the magnitude of the force required to keep the box from sliding down the hill? A box is on the side of a hill inclined at 30 o.What is the vector projection of \(\ \) onto \(\ \)? Sketch the projection.
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