18 Questions
What are two vectors considered equal?
Two vectors are considered equal if they have the same magnitude and direction.
How is the negative of a vector defined?
The negative of a vector has the same magnitude as the given vector but the opposite direction.
How is a vector often represented visually?
A vector is often represented by an arrow or a directed line segment.
What are the different ways to denote a vector?
A vector can be denoted by printing a letter in boldface, putting an arrow above the letter, or underlining the letter.
How is the magnitude of a vector represented visually?
The magnitude of a vector is represented by the length of the arrow from the origin to the point representing the vector.
If a vector is represented by an arrow from the origin to point A, how is the magnitude denoted?
The magnitude of the vector is denoted as OA, a, or a.
What is the negative of a vector?
The negative of a vector is the vector with the same magnitude but in the opposite direction.
How can a vector be represented as a product of its magnitude and unit vector?
A vector can be represented as the product of its magnitude and unit vector in the direction of the vector.
What are the components of a 2-D vector with initial point Q(x1, y1) and terminal point R(x2, y2)?
The components of a 2-D vector are: a1 = x2 - x1; a2 = y2 - y1.
How is a 3-dimensional vector represented in terms of its components?
A 3-dimensional vector is represented as [A1, A2, A3] or [a1, a2, a3].
What is the formula for finding the magnitude or modulus of a vector in 2 dimensions?
For a 2-dimensional vector, the magnitude is given by: a = sqrt(a1^2 + a2^2).
How can a vector be represented using the i, j, k notation for vectors?
A vector can be represented as [a1, a2, a3] or [a1i + a2j + a3k].
Define the standard basis of 3 or rectangular component vectors.
The triple of vectors i, j, k represent the component vectors of a in the x, y, and z directions respectively.
Explain what a position vector is in a Cartesian coordinate system.
The position vector or radius vector r of a point A (x, y, z) is the vector with the origin as the initial point and A as the terminal point, written as r = xi + yj + zk.
What is the magnitude or modulus of a position vector r = [x, y, z]?
The magnitude is given by r = sqrt(x^2 + y^2 + z^2).
Explain why a 2-dimensional vector is called rectangular.
A 2-dimensional vector is called rectangular because there is a right angle between the x and y directions.
Describe the 3-dimensional coordinate system and its axes.
In 3-dimensional space, there are three axes: x-axis (forward), y-axis (right), and z-axis (up).
What is the resultant vector when adding vectors AB and BC?
The sum/resultant of two vectors AB and BC is the single vector AC.
Test your knowledge on vector magnitude and direction. Learn about representing a vector as a product of its magnitude and unit vector, as well as understanding unit vectors and their significance in determining direction.
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