Question

• The length of the projection of the line segment joining (1, 3,-1) and (3, 2, 4) on z axis is
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Answer 1

Answer: √30 units

Given two points in 3d space as,

• A (1, 3, -1) and B (3, 2, 4)

We have to find the distance between the two points or just projection of the line line segment.

In a 3d space, the distance between two points A(x₁, y₁, z₁) and B(x₂, y₂, z₂) is given by the formula,

⇒ AB = √{ (x₂ - x₁)² + (y₂ - y₁)² + (z₂ - z₁)² }

Substituting the required values in the formula, we get

⇒ AB = √{ (3 - 1)² + (2 - 3)² + (4 - (-1))² }

⇒ AB = √{ (2)² + (-1)² + (5)² }

⇒ AB = √( 4 + 1 + 25 )

⇒ AB = √30

∴ The length of projection of the line segment formed by joining the given points is √30 units.

Some Information:-

Distance of two points A(x₁, y₁) and B(x₂, y₂) in a 2d plane is given by,

• AB = √{ (x₂ - x₁)² + (y₂ - y₁)² }

Answer 2

Answer:

• √30 units

Step-by-step explanation:

Given

• Points (3d plane) : A (1, 3,-1) and B (3, 2, 4)

To find

• The length of the projection of the line segment or the distance between two points.

Solution

The distance between two points A and B when on 3d plane is given by,

⇛ AB = √(x₂ - x₁)² + (y₂ - y₁)² + (z₂ - z₁)²

Where:

↪ x₁ = 1

↪ x₂ = 3

↪ y₁ = 3

↪ y₂ = 2

↪ z₁ = -1

↪ z₂ = 4

• √(3 - 1)² + (2 - 3)² + (4 - (-1))²
• √(2)² + (-1)² + (5)²
• √(4 + 1 + 25)
• √30

Hence, the length of projection of the line segment formed by joining the given points is √30 units.