Can We Solve the JEE Questions from Units and Dimensions by Just Only Reading the Unit and Dimensions Chapter of Class 11?

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Vectors are geometrical objects with magnitude and direction. A vector has two points: a beginning point and a terminal point, which reflects the point’s end location. Addition, subtraction, and multiplication are some of the mathematical operations that may be performed on vectors. A unit vector is defined as a vector with a magnitude of one. Vector v = (1,3), for example, is not a unit vector since its magnitude is not equal to one. When we divide any vector by the magnitude of another vector, we get a unit vector. A direction vector can also be referred to as a unit vector. Let’s take a closer look at the unit vector, its formula, and some solved cases.

Unit Vector

Unit vectors are defined as vectors with magnitude equal to one and are denoted by the letter a. Unit vectors have a length of one. Unit vectors are commonly used to indicate a vector’s direction. The Magnitude of a Vector: The numeric value for a particular vector is determined by the magnitude of a vector formula. A vector has both a magnitude and a direction. The magnitude of a vector formula is the total of the vector’s component measurements along the x, y, and z axes. |A| is the magnitude of a vector -A. The magnitude of a vector having directions along the x-axis, y-axis, and z-axis may be calculated by taking the square root of the total of the squares of its direction ratios. Let’s have a look at the below magnitude of a vector formula to see what we’re talking about.

Unit Vector Notation

It is provided by a = a/|a|, where |a| denotes the vector a’s norm or magnitude. A Unit vector formula or a calculator can be used to compute it.

In three dimensions, the unit vectors of I j, and k are generally the unit vectors along the x, y, and z axes, respectively. A linear combination of these unit vectors may be used to express any vector in three-dimensional space. A scalar quantity is always the dot product of two unit vectors. The cross-product of two supplied unit vectors, on the other hand, produces a third vector that is perpendicular (orthogonal) to both of them.

Unit Normal Vector: A ‘normal vector’ is a vector which is perpendicular to the plane at a specified location. A surface containing the vector is also referred to as “normal.” The unit normal vector, sometimes known as the “unit normal,” is the unit vector obtained after normalising the normal vector. We do this by dividing the vector norm of a non-zero normal vector.

Unit Vector Formula

Vectors are indicated with an arrow a, which signifies a unit vector, because they have both magnitude (Value) and direction. We divide the magnitude of a vector by its unit vector to determine its unit vector. Any vector is usually represented by the coordinates x, y, and z. There are two methods to express a vector: a = (x, y, z) using the brackets, and a =x^i + y^j +z^k.

The formula for determining a vector’s magnitude is: |a|= (x2 + y2 + z2). The magnitude of a unit vector is equal to the magnitude of a vector. The formula above is for a unit vector. What is the best way to find the unit vector? Simply divide a given vector by its magnitude to obtain a unit vector with the same direction. Consider a vector with a magnitude of |v|, such as v = (1,4). We may acquire the unit vector v by dividing each component of vector v by |v|, which is in the same direction as v.

Application of Unit Vector

The direction of a vector is specified by unit vectors. In both two and three-dimensional planes, unit vectors can exist. Every vector has a unit vector that may be expressed in the form of its components. A vector’s unit vectors are oriented along the axes. Unit vectors in three-dimensional space are written as v = x + y + z. Three perpendicular axes will be used to identify the vector v in the three-dimensional plane (x, y, and z-axis). The unit vector along the x-axis is denoted by the letter I in mathematical notation. j represents the unit vector along the y-axis, while k represents the unit vector along the z-axis. As a result, the vector v may be expressed as: v = xi^ + yj^ + zk^. Electromagnetics is the study of electric and magnetic forces. In this case, vectors are useful for representing and performing calculations using these forces. Vectors can be used to depict the velocity of an aeroplane or a train in everyday life, when both the speed and direction of travel are required.

 

Learn more about: The resultant of two forces , one double the other in magnitude is perpendicular to the smaller of the two forces. The angle between the two forces is _?

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