Exploring Vector Components and Magnitudes

What are the components of the vector A = 3i + 4j?

• The components of the vector A are 3 (j-component) and 4 (i-component).

• The components of the vector A are 3 (i-component) and 4 (j-component).

• The components of the vector A are 5 (i-component) and 2 (j-component).

• The components of the vector A are 3 (i-component) and 3 (j-component).

Calculate the magnitude of the vector B = 6i - 8j.

• 8

• 12

• 10

• 5

Define a unit vector and provide an example.

• A unit vector is defined as a vector that points in the negative direction.

• An example of a unit vector is (2, 2, 2), which has a magnitude of 3.

• An example of a unit vector is (1, 0, 0), which points in the positive x-direction and has a magnitude of 1.

• A unit vector is any vector with a magnitude of 0.

Express the vector C = 5i + 12j in unit vector form.

• C = (5/13)i + (12/13)j

• C = (5/13)i + (5/12)j

• C = (12/13)i + (5/13)j

• C = (5/12)i + (12/5)j

Resolve the vector D = 10 at an angle of 30 degrees into its components.

• D_x = 5, D_y = 5√3

• D_x = 10, D_y = 0

• D_x = 0, D_y = 10

• D_x = 5√3, D_y = 5

What is the magnitude of the vector E = -2i + 2j?

• 4

• √8

• 2√2

• 2

If F = 7i + 24j, what is the magnitude of F?

• 25

• 30

• 20

• 15

How do you denote a vector in mathematical notation?

• A vector is denoted as **v** or \vec{v}.

• A vector is denoted as **a** or $\vec{a}$.

• A vector is denoted as **x** or $\vec{x}$.

• A vector is denoted as **p** or $\vec{p}$.

What are the components of the vector G = -5i - 5j?

• The components of the vector G are -5 (i-component) and 5 (j-component).

• The components of the vector G are 5 (i-component) and 5 (j-component).

• The components of the vector G are -5 (i-component) and -5 (j-component).

• The components of the vector G are 0 (i-component) and -5 (j-component).

Calculate the magnitude of the vector H = 1i + 1j + 1k.

• 3.000

• 2.000

• 1.732

• 1.414