Skew Lines MCQ Quiz - Objective Question with Answer for Skew Lines - Download Free PDF
Last updated on Jul 4, 2025
Latest Skew Lines MCQ Objective Questions
Skew Lines Question 1:
If the shortest distance between the line joining the points(1, 2, 3) and (2, 3, 4), and the line
Answer (Detailed Solution Below) 18
Skew Lines Question 1 Detailed Solution
Calculation:
⇒
⇒
⇒
⇒
⇒
Now, 28α2 = 28×
Hence, the correct answer is 18.
Skew Lines Question 2:
The shortest distance between the lines x + 1 = 2y = -12z and x = y + 2 = 6z – 6 is
Answer (Detailed Solution Below)
Skew Lines Question 2 Detailed Solution
Calculation:
Hence, the correct answer is Option 1.
Skew Lines Question 3:
If the square of the shortest distance between the lines
Answer (Detailed Solution Below)
Skew Lines Question 3 Detailed Solution
Calculation
=
=
m = 4, n = 5 ⇒ m + n = 9
Hence option 2 is correct
Skew Lines Question 4:
Let L1 :
Answer (Detailed Solution Below)
Skew Lines Question 4 Detailed Solution
Calculation
P(2λ + 1, 3λ + 2, 4λ + 3) on L1
Q(3µ + 2, 4µ + 4, 5µ + 5) on L2
Dr’s of PQ = 3µ – 2λ + 1, 4µ – 3λ + 2, 5µ – 4λ + 2
PQ ⊥ L1
⇒ (3µ – 2λ + 1)2 + (4µ – 3λ + 2)3 + (5µ – 4λ + 2)4 = 0
38µ – 29λ + 16 = 0 …(1)
PQ ⊥ L2
⇒ (3µ – 2λ + 1)3 + (4µ – 3λ + 2)4 + (5µ – 4λ + 2)5 = 0
50µ – 38λ + 21 = 0 …(2)
By (1) & (2)
∴
Line PQ
lies on the line PQ
Hence option 4 is correct
Skew Lines Question 5:
If the line,
Answer (Detailed Solution Below)
Skew Lines Question 5 Detailed Solution
Calculation
Let P be any point on the line,
P lies on the plane
⇒
⇒
⇒
⇒
⇒
Another line is
⇒
⇒
Hence option 1 is correct
Top Skew Lines MCQ Objective Questions
Find the magnitude of the shortest distance between the lines
Answer (Detailed Solution Below)
Skew Lines Question 6 Detailed Solution
Download Solution PDFConcept:
The magnitude of the shortest distance between the lines
Given:
The lines
Rewriting the given equations,
⇒
Therefore, the magnitude of the shortest distance between the given lines is
Therefore, the magnitude of the shortest distance between the given lines is
Let L1 and L2 be two parallel lines with the equations
Answer (Detailed Solution Below)
Skew Lines Question 7 Detailed Solution
Download Solution PDFConcept:
- If two lines are parallel, then the distance between them is fixed.
- The distance between two parallel lines
and is given by the formula: .
Calculation:
Using the formula for the distance between two parallel lines, we can say that the distance is
Find the shortest distance between the lines
Answer (Detailed Solution Below)
Skew Lines Question 8 Detailed Solution
Download Solution PDFConcept:
The shortest distance between the skew line
Calculation:
Given: Equation of lines is
By comparing the given equations with
⇒ x1 = 8, y1 = - 9, z1 = 10, a1 = 3, b1 = -16 and c1 = 7
Similarly, x2 = 15, y2 = 29, z2 = 5, a2 = 3, b2 = 8 and c2 = -5
So,
As we know that shortest distance between two skew lines is given by:
⇒ SD = 14 units
Hence, option B is the correct answer.
Find the shortest distance between the lines whose vector equations are
Answer (Detailed Solution Below)
Skew Lines Question 9 Detailed Solution
Download Solution PDFConcept:
The shortest distance between parallel lines
Calculation:
L1:
L2:
Here, we see both lines are parallel and
⇒
⇒
Hence, option 1 is correct.
Find the shortest distance between the lines whose vector equations are
Answer (Detailed Solution Below)
Skew Lines Question 10 Detailed Solution
Download Solution PDFConcept:
The shortest distance between parallel lines
Calculation:
L1:
L2:
Here, we see both lines are parallel and
⇒
⇒
Hence, option 1 is correct.
Find the shortest distance between the lines
Answer (Detailed Solution Below)
Skew Lines Question 11 Detailed Solution
Download Solution PDFConcept:
The shortest distance between the lines
Calculation:
Here we have to find the shortest distance between the lines
Let line L1 be represented by the equation
⇒ x1 = 0, y1 = 2, z1 = 0 and a1 = -1, b1 = 0, c1 = 1.
⇒ x2 = -2, y2 = 0, z2 = 0 and a2 = 1, b2 = 1, c2 = 0.
∵ The shortest distance between the lines is given by:
⇒
⇒
⇒ d = 0
Hence, option 4 is correct.
If the shortest distance between parallel lines
Answer (Detailed Solution Below)
Skew Lines Question 12 Detailed Solution
Download Solution PDFConcept:
The shortest distance between parallel lines
Calculation:
Given: Equation of lines
So, by comparing the above equations with
⇒
⇒
⇒
⇒
⇒ k = 20
Hence, option 4 is correct.
Find the shortest distance between the lines
Answer (Detailed Solution Below)
Skew Lines Question 13 Detailed Solution
Download Solution PDFConcept:
The shortest distance between the skew line
Calculation:
Given: Equation of lines is
By comparing the given equations with
⇒ x1 = - 3, y1 = 6, z1 = 0, a1 = - 4, b1 = 3 and c1 = 2
Similarly, x2 = - 2, y2 = 0, z2 = 7, a2 = - 4, b2 = 1 and c2 = 1
So,
Similarly,
As we know that shortest distance between two skew lines is given by:
Answer (Detailed Solution Below)
Skew Lines Question 14 Detailed Solution
Download Solution PDFConcept -
Shortest distance between two lines is:
d =
Explanation -
The given lines are :
So,
∴
=
=
Shortest distance,
=
=
Hence Option (2) is correct.
Find the shortest distance between the lines
Answer (Detailed Solution Below)
Skew Lines Question 15 Detailed Solution
Download Solution PDFConcept:
The shortest distance between the lines
Calculation:
Here we have to find the shortest distance between the lines
Let line L1 be represented by the equation
⇒ x1 = 5, y1 = -2, z1 = 0 and a1 = 7, b1 = -5, c1 = 1.
⇒ x2 = 0, y2 = 0, z2 = 0 and a2 = 1, b2 = 2, c2 = 3.
∵ The shortest distance between the lines is given by:
⇒
⇒
⇒
⇒
Hence, option 3 is correct.