Direction of a Vector Examples

Example 1: Calculate the direction of the vector if vertical displacement is 5 and horizontal displacement is 4. 

Solution:

We have,

• y = 5
• x = 4

Using the formula we get,

θ = tan^-1 (y/x)

θ = tan^-1 (5/4) = 51.34°

Example 2: Calculate the direction of the vector if vertical displacement is 7 and horizontal displacement is 5.

Solution:

We have,

• y = 7
• x = 5

Using the formula we get,

θ = tan^-1 (y/x)

θ = tan^-1 (7/5) = 54.46°

Example 3: Calculate the vertical displacement if the direction of the vector is 60° and the horizontal displacement is 5.

Solution:

We have,

• θ = 60°
• x = 5

Using the formula we get,

tan θ = y/x

=> y = x tan θ

y = 5 tan 60° = 8.66

Examples 4: Calculate the vertical displacement if the direction of the vector is 30° and the horizontal displacement is 8.

Solution:

We have,

• θ = 30°
• x = 8

Using the formula we get,

tan θ = y/x

=> y = x tan θ

y = 8 tan 30° = 4.61

Example 5: Calculate the horizontal displacement if the direction of the vector is 50° and the vertical displacement is 4.

Solution:

We have,

• θ = 50°
• x = 4

Using the formula we get,

tan θ = y/x

=> x = y/tan θ

x = 4/tan 50° = 3.35

Example 6: Calculate the horizontal displacement if the direction of the vector is 45° and the vertical displacement is 9.

Solution:

We have,

• θ = 45°
• x = 9

Using the formula we get,

tan θ = y/x

=> x = y/tan θ

x = 9/tan 45° = 9/1 = 9

Example 7: Calculate the direction of the vector for the initial point (8, 4) and final point (10, 6).

Solution:

We have,

• (x₁, y₁) = (8, 4)
• (x₂, y₂) = (10, 6)

Find the vertical displacement.

y = y₂ – y₁ 

= 6 – 4 = 2

Find the horizontal displacement.

x = x₂ – x₁

x = 10 – 8 = 2

Using the formula we get,

θ = tan^-1 (y/x)

θ = tan^-1 (2/2)

θ = tan^-1 (1) = 45°

A vector is formed when two distinct points are joined with each other. The point from which a line was drawn to the other point determines the direction of that vector. A vector’s direction is the angle formed by the vector with the horizontal axis, also known as the X-axis. It is provided by the counterclockwise rotation of the vector’s angle about its tail due east. In other words, the orientation of a vector, that is, the angle it makes with the x-axis, is defined as its direction.

In this article we will learn about, Direction of Vector Definition, Direction of Vector Formula, Magnitude of Vector, Examples, and others in detail.