The answer below assumes you are required to find the components of the vector.
A vector with unity magnitude means that the magnitude of the vector equals to 1. Therefore its a simple case of calculating the values of sin(45) for the vertical components and cos(45) for the horizontal components.
Both of these values equal to 1/sqrt(2) {one over square-root two}
If a vector, of magnitude v, makes an angle of Φ with the adjacent side then the adjacent component = v*cos(Φ), and opposite component = v*sin(Φ)
Yes, acceleration can be positive and negative because acceleration is a vector. It has both direction and magnitude. The direction is what makes it positive or negative. Negative acceleration is usually called deceleration.
yes, the slope of the line is the tangent of the angle
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Scalar QuantitiesMost of the physical quantities encountered in physics are either scalar or vector quantities. A scalar quantity is defined as a quantity that has magnitude only. Typical examples of scalar quantities are time, speed, temperature, and volume. A scalar quantity or parameter has no directional component, only magnitude. For example, the units for time (minutes, days, hours, etc.) represent an amount of time only and tell nothing of direction. Additional examples of scalar quantities are density, mass, and energy.Vector QuantitiesA vectorquantity is defined as a quantity that has both magnitude and direction. To work with vector quantities, one must know the method for representing these quantities. Magnitude, or "size" of a vector, is also referred to as the vector's "displacement." It can be thought of as the scalar portion of the vector and is represented by the length of the vector. By definition, a vector has both magnitude and direction. Direction indicates how the vector is oriented relative to some reference axis, as shown in Figure 1. Using north/south and east/west reference axes, vector "A" is oriented in the NE quadrant with a direction of 45 north of the o EW axis. G iving direction to scalar "A" makes it a vector. The length of "A" is representative of its magnitude or displacement.Another AnswerA scalar quantity refers only to the magnitude of the quantity and answers the question how much. Ex. height, weight, volume, and the like. 2 lbs of sugar is scalar, 4 m long is scalarA vector quantity refers to both magnitude and direction and answers how much and where is it going, (in that sense)Ex. forces, velocity. 200 km/hr at N30degE is a vector, the force required to push a drum up or down a ramp is a vector, the force exerted by the cue stick in billiards is a vector a scalar is a number, like a distance... like the moon is 300.000km away from earth.a vector is a number AND a direction. It's like "moving east at 100km/h"while "moving at 100km/h" alone is a scalar.The idea is that a scalar has only ONE dimension, while a vector has several.
This isn't a simple yes or no question.An angle is a scalar quantity, and a vector is a ... well, vector... quantity. However, there is a relation between the two, and in two dimensions (for example) it's possible to specify a vector in terms of its magnitude and a "vector angle"; that is, the angle it makes with an axis (generally the x-axis, by convention) of the coordinate system.Sometimes the word "vector" is used in a non-mathematical sense to simply mean a direction, not a magnitude. (One example would be in navigation, where the "vector" to another object is the direction it's in; range is treated separately, though in the mathematical sense vector encompasses both direction and range.) In this case it can be more or less equivalent to an angle.
A vector is created by pointing in a particular direction by specifying its magnitude (length) and direction. The vector's direction is defined by the angle it makes with a reference axis (like north, east, or up), while the magnitude represents the length of the arrow pointing in that direction.
Suppose the magnitude of the vector is V and its direction makes an angle A with the x-axis, then the x component is V*Cos(A) and the y component is V*Sin(A)
Yes, vectors must have the direction. Without direction, it is simply a scalar quantity.
If a vector, of magnitude v, makes an angle of Φ with the adjacent side then the adjacent component = v*cos(Φ), and opposite component = v*sin(Φ)
Yes, acceleration can be positive and negative because acceleration is a vector. It has both direction and magnitude. The direction is what makes it positive or negative. Negative acceleration is usually called deceleration.
Scalar and vector quantities are both used in physics to describe properties of objects. They both have magnitude, which represents the size or amount of the quantity. However, the key difference is that vector quantities also have direction associated with them, while scalar quantities do not.
the radius vector; and the vectorial angle the radius vector; and the vectorial angle
Magnitude and diction. Aka a vector:>(that was for all the Despicable Me lovers)
Representing a vector quantity by an arrow helps to visualize its magnitude and direction. The length of the arrow represents the magnitude of the vector, and the direction of the arrow indicates the direction of the vector. This visual representation makes it easier to understand vector operations and relationships.
A dipole moment is a vector quantity because it has both magnitude and direction. It describes the separation of positive and negative charges within a molecule, with the direction pointing from the negative to the positive end of the dipole. This directionality makes it necessary to represent the dipole moment as a vector.
Consider vectors A and B. A has magnitude s and makes an angle a with the positive direction of the x-axis. B has magnitude t and makes an angle b with the positive direction of the x-axis. Then the components of A and B along the x-axis are, respectively, s*cos(a) and t*cos(b). Thus the total horizontal component is u = s*cos(a) and t*cos(b). The components of A and B along the y-axis are, respectively, s*sin(a) and t*sin(b). Thus the total vertical component is v = s*sin(a) and t*sin(b). The magnitude of the resultant, by Pythagoras, is then sqrt(u2 + v2)