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MAT Vectors & 3D Geometry — practice questions — page 2

Explore 43 free Vectors & 3D Geometry questions in MAT Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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Vectors & 3D Geometry questions and exercises with answers

Showing questions 31–43 of 43.

Parallel, perpendicular, or neither?Read the answer and worked solution →True or false: parallel and perpendicularRead the answer and worked solution →Order the steps: test three points for collinearityRead the answer and worked solution →Assertion and reasonRead the answer and worked solution →Two are true, one is notRead the answer and worked solution →Three of these are wrong. Find the one that holds.Read the answer and worked solution →Which test applies?Read the answer and worked solution →Flip and pair: condition with conclusionRead the answer and worked solution →Tap every statement true of slopeRead the answer and worked solution →Reading the definitions backRead the answer and worked solution →Spot the one that does not belongRead the answer and worked solution →Complete the angle between two linesRead the answer and worked solution →True or false: using coordinatesRead the answer and worked solution →

Worked practice questions

Parallel, perpendicular, or neither?

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Questions
  1. Question
    Two lines with equal slopes are
    Choices
    1. perpendicular
    2. parallel
    3. neither
    Correct choice
    parallel
  2. Question
    Two lines whose slopes multiply to −1 are
    Choices
    1. parallel
    2. neither
    3. perpendicular
    Correct choice
    perpendicular
  3. Question
    Slopes 2 and −1/2 mean the lines are
    Choices
    1. perpendicular
    2. parallel
    3. neither
    Correct choice
    perpendicular
  4. Question
    Slopes 3 and 3 mean the lines are
    Choices
    1. perpendicular
    2. parallel
    3. neither
    Correct choice
    parallel
Two conditions decide it. Source: syllabus Maths, Ch 9 Straight Lines.

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True or false: parallel and perpendicular

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Questions
  1. Statement is true
    Yes
    Statement
    Two lines are parallel if and only if their slopes are equal.
  2. Statement is true
    Yes
    Statement
    Two lines are perpendicular if and only if their slopes multiply to −1.
  3. Statement is true
    No
    Statement
    Perpendicular lines have equal slopes.
  4. Statement is true
    No
    Statement
    Parallel lines have slopes multiplying to −1.
  5. Statement is true
    Yes
    Statement
    Three points are collinear when slope AB equals slope BC.
Both tests are 'if and only if', so they run in both directions. Source: syllabus Maths, Ch 9 Straight Lines.

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Order the steps: test three points for collinearity

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Steps
  1. Label the three points A, B and C
  2. Compute the slope of AB from the coordinate differences
  3. Compute the slope of BC the same way
  4. Compare the two slopes
  5. If they are equal, the three points are collinear
Two slopes, compared. Source: syllabus Maths, Ch 9 Straight Lines.

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