Question

Consider the vectors. Which pairs (if any) of these vectors are

a) Collinear
b) Orthogonal
c) Coplanar
d) Linearly independent

Answer 1

The vectors are collinear, orthogonal, coplanar, and not linearly independent.

Step-by-step explanation:

The vectors are given as:
a. All three are parallel to each other and are along the x-axis.
b. All three are mutually perpendicular to each other.
In this case, we can determine the properties of the vectors as follows:

1. a) Collinear: Since all the vectors are parallel to each other and lie along the same axis (x-axis), they are collinear.
2. b) Orthogonal: Since all the three vectors are mutually perpendicular to each other, they are orthogonal.
3. c) Coplanar: Since the vectors lie on the same plane (x-y plane), they are coplanar.
4. d) Linearly Independent: The vectors are not linearly independent, as they all lie on the same line and therefore can be expressed as multiples of each other.