JEE Advanced Vector Algebra and 3D Geometry — practice questions — page 5

Explore 126 free Vector Algebra and 3D Geometry questions in JEE Advanced Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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Vector Algebra and 3D Geometry questions and exercises with answers

Showing questions 121–126 of 126.

Skew linesRead the answer and worked solution →Tap every pair of lines that could be skewRead the answer and worked solution →A UNIT VECTOR in the direction of v = 3i + 4j is:Read the answer and worked solution →True or false: vectors and 3DRead the answer and worked solution →Three of these are wrong. Find the one that holds.Read the answer and worked solution →Spot the odd one outRead the answer and worked solution →

Worked practice questions

Skew lines

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Questions

Question
Skew lines are
Choices
1. parallel but not equal
2. intersecting at right angles
3. neither parallel nor intersecting
Correct choice
neither parallel nor intersecting
Question
Two skew lines lie
Choices
1. in different planes
2. in the same plane
3. always on the x-axis
Correct choice
in different planes
Question
Can two skew lines ever meet?
Choices
1. Yes, at one point
2. No
3. Only at the origin
Correct choice
No
Question
The angle between skew lines is measured using
Choices
1. the distance between them
2. their midpoints
3. intersecting lines drawn parallel to each
Correct choice
intersecting lines drawn parallel to each

Your syllabus defines skew lines as lines in space that are neither parallel nor intersecting, and notes they lie in different planes. Source: syllabus Maths Part II, Ch 11 Three Dimensional Geometry.

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Tap every pair of lines that could be skew

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Questions

Items
1. Text
  Two lines in space that never meet and are not parallel
  Matches the category
  Yes
2. Text
  Two lines lying in different planes, never meeting
  Matches the category
  Yes
3. Text
  Two parallel lines
  Matches the category
  No
4. Text
  Two lines crossing at a point
  Matches the category
  No
5. Text
  Two lines in the same plane that never meet
  Matches the category
  No
Category
Could be a pair of SKEW lines

Skewness rules out both meeting and being parallel so it can only happen in three dimensions. Source: syllabus Maths Part II, Ch 11 Three Dimensional Geometry.

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A UNIT VECTOR in the direction of v = 3i + 4j is:

$(3i + 4j)/5$
$(3i + 4j)/7$
$3i + 4j$ itself
$5(3i + 4j)$

Show answer and solution

Correct answer: A. $(3i + 4j)/5$

|v| = √(9+16) = √25 = 5. Unit vector v̂ = v/|v| = (3i + 4j)/5 = (0.6)i + (0.8)j.

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