Shortest Distance MCQ Quiz in தமிழ் - Objective Question with Answer for Shortest Distance - இலவச PDF ஐப் பதிவிறக்கவும்

Concept:

The shortest distance between the skew line  is given by:

Calculation:

Given: Equation of lines is 

By comparing the given equations with , we get

⇒ x1 = 3, y1 = 4, z1 = - 2, a1 = -1, b1 = 2 and c1 = 1

Similarly, x2 = 1, y2 = - 7, z2 = -2, a2 = 1, b2 = 3 and c2 = 2

So, 

As we know that shortest distance between two skew lines is given by:

⇒ 

Hence, option C is the correct answer.

Calculation:

Distance between skew lines  and  is given by:

d = 

Calculation:

Given, (x – λ)/1 = (y – 1/2)/(1/2) = z/(-1/2)

(x – λ)/2 = (y-1/2)/1 = z/(-1) …(1) Point on line = (λ, 1/2, 0)

x/1 = (y + 2λ)/1 = (z – λ)/1 …(2) Point on line = (0, -2λ, λ)

∴ Distance between skew lines = 

= 

= |-5λ – 3/2|/

= √7/(2√2) (Given)

⇒ |10λ + 3| = 7

⇒ 10λ + 3 = ± 7

⇒ λ = - 1 [∵ λ is an integer]

⇒ |λ| = 1

∴ The value of |λ| is 1. 

Concept:

The shortest distance between the lines  and  is given by d = 

Calculation:

Given,  and 

∴ a₁ =  and b₁ = 

a₂ =  and b₂ = 

⇒ a₂ – a₁ = 

∴ 

= 

⇒ 

∴  = 16[-4 + 16] = (16)(12)

⇒ d =  = 4√3

∴ The shortest distance is 4√3.

The correct answer is Option 2.

Calculation

⇒ 

⇒ 

⇒ 

⇒ 

Hence, Option (3) is correct

Calculation

Given

d₁ = shortest distance between L₁ & L₂ 

⇒ d₁= 

⇒ d₁ = 2

d₂ = shortest distance between L₃ & L₄

⇒  

Hence

 = 16

Concept:

The shortest distance between the skew line and  is given by:

Calculation:

Given: Equation of lines is  and 

By comparing the given equations with  and , we get

⇒ x1 = 12, y1 = 1, z1 = 5, a1 = -9, b1 = 4 and c1 = 2

Similarly, x2 = 23, y2 = 19, z2 = 25, a2 = -6, b2 = -4 and c2 = 3

So, 

As we know that shortest distance between two skew lines is given by:

⇒ SD = 26 units

Hence, option A is the correct answer.

Concept:

The shortest distance between the skew line  is given by:

Calculation:

Given: The equation of lines is 

By comparing the given equations, we get

⇒ x1 = 3, y1 = 5, z1 = 7, a1 = 1, b1 = - 2 and c1 = 1

Similarly, x2 = - 1, y2 = -1, z2 = -1, a2 = 7, b2 = - 6 and c2 = 1

So, 

Similarly, 

= 2√29

As we know that shortest distance between two skew lines is given by:

⇒ SD = 

Calculation

Let P be any point on the line,

P lies on the plane

⇒ 

⇒ 

⇒ 

⇒ 

⇒ 

Line is

Another line is (line ) Shortest distance be d.

⇒  where are DRS of lines

⇒ 

Hence option 1 is correct

Calculation

Given: Shortest distance(S.D) = 1

Passing points of lines L₁ & L₂ are

(λ, 2, 1) & (√3, 1, 2)

⇒ 

⇒ λ = 0, λ = 2√3

∴ The sum of all possible values of λ is 

Explanation -

Shortest dist. = 

144 + 16λ² + (3λ – 6)² = 169

16λ² + (3λ – 6)² = 25  ⇒ λ = 1 

Hence Option (3) is correct.