FAQs on L3 - Introduction to Vectors Video Lecture - Additional Study Material for NEET
|1. What is a vector in mathematics?
Ans. A vector is a mathematical object that has both magnitude and direction. It can be represented by an arrow, where the length of the arrow represents the magnitude and the direction of the arrow represents the direction of the vector.
|2. How are vectors represented in three-dimensional space?
Ans. In three-dimensional space, vectors can be represented using three coordinates (x, y, z) or by their corresponding components along the x, y, and z axes. For example, a vector v can be represented as v = (x, y, z) or v = xi + yj + zk, where i, j, and k are the unit vectors along the x, y, and z axes respectively.
|3. What is the difference between a scalar quantity and a vector quantity?
Ans. A scalar quantity only has magnitude, while a vector quantity has both magnitude and direction. For example, temperature is a scalar quantity as it only has magnitude (e.g., 25 degrees Celsius), whereas displacement is a vector quantity as it has both magnitude (e.g., 10 meters) and direction (e.g., north).
|4. How do you add two vectors together?
Ans. To add two vectors together, you can use the parallelogram rule or the head-to-tail method. In the parallelogram rule, you draw the vectors as adjacent sides of a parallelogram and the resultant vector is the diagonal of the parallelogram. In the head-to-tail method, you place the tail of the second vector at the head of the first vector and the resultant vector is the vector from the tail of the first vector to the head of the second vector.
|5. Can vectors be multiplied?
Ans. Yes, vectors can be multiplied, but there are different types of vector multiplication. The dot product (or scalar product) of two vectors gives a scalar quantity, while the cross product (or vector product) of two vectors gives a vector quantity. The dot product is defined as the product of the magnitudes of the vectors and the cosine of the angle between them, while the cross product is defined as the product of the magnitudes of the vectors, the sine of the angle between them, and a unit vector perpendicular to the plane of the two vectors.