Shortest Distance MCQ Quiz in मल्याळम - Objective Question with Answer for Shortest Distance - സൗജന്യ PDF ഡൗൺലോഡ് ചെയ്യുക
Last updated on Mar 19, 2025
Latest Shortest Distance MCQ Objective Questions
Top Shortest Distance MCQ Objective Questions
Shortest Distance Question 1:
Find the shortest distance between the lines
Answer (Detailed Solution Below)
Shortest Distance Question 1 Detailed Solution
Concept:
The shortest distance between the skew line
Calculation:
Given: Equation of lines is
By comparing the given equations with
⇒ 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.
Shortest Distance Question 2:
Let λ be an integer. If the shortest distance between the lines x – λ = 2y – 1 = -2z and x = y + 2λ = z – λ is √7/2√2, then the value of |λ| is _________
Answer (Detailed Solution Below) 1
Shortest Distance Question 2 Detailed Solution
Calculation:
Distance between skew lines
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.
Shortest Distance Question 3:
The shortest distance between the lines
Answer (Detailed Solution Below)
Shortest Distance Question 3 Detailed Solution
Concept:
The shortest distance between the lines
Calculation:
Given,
∴ a1 =
a2 =
⇒ a2 – a1 =
∴
=
⇒
∴
⇒ d =
∴ The shortest distance is 4√3.
The correct answer is Option 2.
Shortest Distance Question 4:
The shortest distance between lines L1 and L2, where
Answer (Detailed Solution Below)
Shortest Distance Question 4 Detailed Solution
Calculation
⇒
⇒
⇒
⇒
Hence, Option (3) is correct
Shortest Distance Question 5:
If d1 is the shortest distance between the lines x + 1 = 2y = -12z, x = y + 2 = 6z – 6 and d2 is the shortest distance between the lines
Answer (Detailed Solution Below) 16
Shortest Distance Question 5 Detailed Solution
Calculation
Given
d1 = shortest distance between L1 & L2
⇒ d1=
⇒ d1 = 2
d2 = shortest distance between L3 & L4
⇒
Hence
Shortest Distance Question 6:
Find the shortest distance between the lines
Answer (Detailed Solution Below)
Shortest Distance Question 6 Detailed Solution
Concept:
The shortest distance between the skew line
Calculation:
Given: Equation of lines is
By comparing the given equations with
⇒ 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.
Shortest Distance Question 7:
Find the shortest distance between the lines
Answer (Detailed Solution Below)
Shortest Distance Question 7 Detailed Solution
Concept:
The shortest distance between the skew line
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 =
Shortest Distance Question 8:
If the shortest distance between the lines
Answer (Detailed Solution Below)
Shortest Distance Question 8 Detailed Solution
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
Shortest Distance Question 9:
If the shortest distance between the lines
Answer (Detailed Solution Below)
Shortest Distance Question 9 Detailed Solution
Explanation -
Shortest dist. =
144 + 16λ2 + (3λ – 6)2 = 169
16λ2 + (3λ – 6)2 = 25 ⇒ λ = 1
Hence Option (3) is correct.
Shortest Distance Question 10:
The distance of the point Q(0, 2, –2) form the line passing through the point P(5, –4, 3) and perpendicular to the lines
Answer (Detailed Solution Below)
Shortest Distance Question 10 Detailed Solution
Calculation
l1 :
l2 :
Vector ⊥ to the above two lines
⇒
Equation of required line
⇒ L :
⇒ L :
⇒ x =λ + 5 , y = λ - 4, z = λ + 3
QR.L = (λ + 5).1 + (λ - 6).1 +(3 - λ + 2)(-1) = 0
⇒ 3λ = 6 ⇒ λ = 2
⇒ R = (7, -2, 1)
QR =
Hence option 4 is correct