SCALAR: physical quantities which can be defined by its magnitude only is called scalar quantity.
Example -mass, length, time, distance, speed etc.
VECTOR: Physical quantities which can be defined by its magnitude and direction,which followed vector law of addition is called vector quantity.
Example -displacement, velocity, acceleration, force, momentum etc.
🌟 Current is scalar quantity even it's has magnitude with direction because it does not follow vector law of addition.
Notation of vector given below in image -
length of arrow shows magnitude of vectors and head indicates direction of vector.TYPE OF VECTOR.
(1) PARALLEL VECTOR: If two vector are in same direction , then it is called parallel vectors.
angle between vector AB and vector CD =0°(2). EQUAL VECTOR: If two has it same magnitude and same unit and dimension will be equal vector.If there is in same direction.
If AB vector parallel to CD vector.
then, AB =CD. (AB and CD represent same quantity)
Therefore , vector AB=vector CD
(3) NEGATIVE OF A VECTOR: If a vector is rotated by 180° ,then it is become it's negative vector.
magnitude of opposite vector is equal 
net force is zero Introduction: Welcome to our blog, aimed at helping Class 11 students tackle vector-related questions! Vectors are an important topic in mathematics and physics, and understanding them thoroughly is crucial for success in these subjects. In this blog, we will cover some common and special questions on vectors that Class 11 students may encounter in their studies. So, let's dive in and explore this fascinating topic!
What is a vector? A vector is a quantity that has both magnitude and direction. It is represented by an arrow or a line segment with an initial point and a terminal point. Vectors can be added, subtracted, and multiplied by a scalar, and they play a fundamental role in various fields of science, engineering, and mathematics.
How to represent vectors? There are different ways to represent vectors, including:
a. Geometrically: Vectors can be represented as arrows or line segments with direction and magnitude.
b. Algebraically: Vectors can be represented using Cartesian coordinates, where a vector is expressed as an ordered pair (x, y) or (x, y, z) in 2D or 3D space, respectively.
How to find the magnitude of a vector? The magnitude of a vector is the length of the vector and is denoted by ||v||, where v is the vector. In 2D space, the magnitude of a vector (x, y) can be found using the Pythagorean theorem as ||v|| = √(x^2 + y^2). In 3D space, the magnitude of a vector (x, y, z) can be found as ||v|| = √(x^2 + y^2 + z^2).
How to find the direction of a vector? The direction of a vector is given by the angle it makes with a reference axis or another vector. In 2D space, the direction of a vector (x, y) can be found using trigonometry as θ = atan2(y, x), where atan2(y, x) is the inverse tangent function. In 3D space, the direction of a vector (x, y, z) can be found using spherical coordinates.
How to add and subtract vectors? Vectors can be added and subtracted using the head-to-tail or parallelogram law. To add two vectors, place the tail of the second vector at the head of the first vector, and the resulting vector is the vector from the tail of the first vector to the head of the second vector. To subtract two vectors, add the negative of the second vector to the first vector.
How to multiply vectors by a scalar? Vectors can be multiplied by a scalar, which is a real number. When a vector is multiplied by a scalar, its magnitude is multiplied by the scalar, and its direction remains unchanged. For example, if v is a vector and c is a scalar, then cv is a new vector with a magnitude of c times the magnitude of v and the same direction as v.
What are unit vectors? Unit vectors are vectors with a magnitude of 1. They are often used to represent direction or orientation. In 2D space, the unit vectors i and j represent the x-axis and y-axis, respectively. In 3D space, the unit vectors i, j, and k represent the x-axis, y-axis, and z-axis, respectively.
How to find the dot product and cross product of vectors? The dot product and cross product are two important operations on vectors:
a. Dot product: The dot product of two vectors is a scalar quantity given by the formula a
Vectors are an important topic in mathematics and physics, and it's crucial to have a solid understanding of the concept to excel in these subjects. In this blog post, we'll cover some special questions of vectors that are frequently asked in class 11th exams.
Finding the magnitude of a vector: The magnitude of a vector is its length or size. To find the magnitude of a vector, you need to use the Pythagorean theorem. For example, if the vector is (3, 4), then the magnitude is √(3^2 + 4^2) = 5.
Finding the direction of a vector: The direction of a vector is given by the angle it makes with the positive x-axis. To find the direction, use the formula tan⁻¹(y/x), where x and y are the x and y components of the vector.
Adding and subtracting vectors: To add or subtract vectors, you need to add or subtract their corresponding components. For example, if vector A = (2, 3) and vector B = (4, 1), then A + B = (2 + 4, 3 + 1) = (6, 4), and A - B = (2 - 4, 3 - 1) = (-2, 2).
Finding the dot product of two vectors: The dot product of two vectors A and B is given by A.B = |A||B| cosθ where θ is the angle between the vectors. To find the dot product, multiply the corresponding components and add them up. For example, if vector A = (2, 3) and vector B = (4, 1), then A.B = 2×4 + 3×1 = 11.
Finding the cross product of two vectors: The cross product of two vectors A and B is another vector that is perpendicular to both A and B. The magnitude of the cross product is given by |AxB| = |A||B| sinθ where θ is the angle between the vectors. To find the cross product, use the formula i(j₁k₂ - k₁j₂) - j(i₁k₂ - k₁i₂) + k(i₁j₂ - j₁i₂), where i, j, and k are the unit vectors along the x, y, and z axes, and i₁, j₁, k₁, i₂, j₂, and k₂ are the components of vectors A and B.
Finding the projection of a vector onto another vector: The projection of a vector A onto another vector B is given by (A.B/|B|²)B. To find the projection, first find the dot product of A and B, then divide by the magnitude of B squared, and finally multiply by B.
These are some of the special questions of vectors that you should be familiar with for your class 11th exams. Practice these problems and you'll be well-prepared to tackle any vector-related question that comes your way. Good luck!
