Question

Suppose u and v are two vectors in ℝⁿ. Which of the following is/are true? (Select all that apply.)

I. If c is a scalar, then the distance between u and v is
II. If u and v are orthogonal, then a unit vector in the direction of nonzero vector v is
III. If , then or

a) I and II
b) II only
c) III only
d) I, II, and III

Answer 1

The provided reference question is about distinguishing between vectors and scalars. Displacement and velocity are vectors since they include direction and magnitude, while speed is a scalar because it has only magnitude.

Step-by-step explanation:

The student's question pertains to the properties of vectors and scalars in the field of mathematics, specifically within vector algebra. To address the incomplete question, we can discuss the qualities of vectors, which include having both magnitude and direction, whereas scalars have only magnitude. When a vector is multiplied by a scalar, the direction stays the same if the scalar is positive, and the direction reverses if the scalar is negative. Orthogonal vectors have a 90-degree angle between them, meaning they are perpendicular. If two vectors are orthogonal, the dot product is zero. Knowledge of these properties helps us understand how to perform operations with vectors, such as adding them to find resultant vectors and working with unit vectors in particular coordinate systems.

Answering the reference question provided:

1. Choice d (displacement, speed, velocity) contains two vectors (displacement and velocity) and one scalar (speed).

Displacement and velocity are vectors because they have both magnitude and direction, while speed, being the magnitude of velocity, lacks direction and is thus a scalar.