Vectors and Scalars in Physics

Questions and Answers

A scalar has only magnitude, while a vector has both magnitude and direction.

By splitting it into i and j components, which represent the horizontal and vertical directions respectively.

The resultant vector is the vector obtained by adding together the i and j components of a vector.

The dot product is used to find the angle between two vectors, and it gives a scalar answer. Signup and view all the answers

The dot product of two perpendicular vectors is equal to 0. Signup and view all the answers

By expressing it in terms of its magnitude and direction. Signup and view all the answers

To express a vector in terms of its i and j components. Signup and view all the answers

Speed is a scalar quantity, while velocity is a vector quantity. Signup and view all the answers

By adding them 'tip to tail'. Signup and view all the answers

An arrow over the letter, like this: Signup and view all the answers

Study Notes

A scalar is a quantity with only magnitude, like a normal number, and speed is an example of a scalar.
A vector is a quantity with both magnitude and direction, and velocity is an example of a vector.
Distance is a scalar that measures the length of the path traveled, while displacement is a vector that measures how far an object is from its starting point.

Vectors can be represented as arrows and are often denoted with an arrow over the letter.
Two vectors are equal if and only if they have the same direction and magnitude.
A vector can be multiplied by a scalar, which scales its length.
Vectors can be added "tip to tail".

The i-j plane is a way to express a vector using only numbers by splitting the plane into two perpendicular axes, i and j.
Every vector in a 2D plane can be broken down into its i and j components, which describe how much it goes across (i direction) and how much it goes up (j direction).
Resolving a vector into its components is a way to describe it, and the opposite of this is finding the resultant vector.

The resultant vector is the result of adding a vector's i and j components.
There are two ways to describe a vector: rectangular form (using i and j) and polar form (using magnitude and direction).

The dot product is a way to multiply vectors, and it gives a scalar answer.
The dot product is commutative, meaning the order of the vectors does not matter.
The dot product can be used to find the angle between two vectors using the formula: a · b = |a| |b| cos(θ).
If two vectors are perpendicular, their dot product is equal to 0, because cos(90) = 0.