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Agniveer Air Force Vector Algebra — practice questions — page 2

Explore 41 free Vector Algebra questions in Agniveer Air Force Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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Vector Algebra questions and exercises with answers

Showing questions 31–41 of 41.

Three of these are wrong. Find the one that holds.Read the answer and worked solution →Position vectors and magnitudeRead the answer and worked solution →Tap every statement true of the cross productRead the answer and worked solution →Flip and pair: symbol with meaningRead the answer and worked solution →Complete the component-form rulesRead the answer and worked solution →Order the steps: find the angle between two vectorsRead the answer and worked solution →Sort by what each formula gives youRead the answer and worked solution →True or false: adding vectorsRead the answer and worked solution →Spot the odd one outRead the answer and worked solution →Assertion and reason: productsRead the answer and worked solution →Reading the vocabulary backRead the answer and worked solution →

Worked practice questions

Three of these are wrong. Find the one that holds.

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Questions
  1. Question
    Three of these statements about a · b are false.
    Choices
    1. Item
      It equals |a||b| cos θ
      Correct
      Yes
    2. Explanation
      Sine belongs to the cross product.
      Item
      It equals |a||b| sin θ
    3. Explanation
      The scalar product returns a number.
      Item
      It returns a vector
    4. Explanation
      A number has no direction to be perpendicular to.
      Item
      It is perpendicular to a and b
  2. Question
    Three of these statements about the zero vector are false.
    Choices
    1. Item
      Its initial and terminal points coincide
      Correct
      Yes
    2. Explanation
      That describes a unit vector.
      Item
      It has magnitude 1
    3. Explanation
      It cannot be assigned any definite direction.
      Item
      It points along the x-axis
    4. Explanation
      Their magnitudes are 0 and 1 respectively.
      Item
      It is the same as a unit vector
Each trap swaps the two products or forgets what the zero vector cannot do. Source: syllabus Maths Part II, Ch 10 Vector Algebra.

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Position vectors and magnitude

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Questions
  1. Question
    Magnitude of the position vector of P(x, y, z)
    Choices
    1. √(x² + y² + z²)
    2. x + y + z
    3. x² + y² + z²
    Correct choice
    √(x² + y² + z²)
  2. Question
    The scalar components of a vector are also its
    Choices
    1. direction cosines
    2. direction ratios
    3. magnitudes
    Correct choice
    direction ratios
  3. Question
    Direction cosines are obtained from ratios by dividing by
    Choices
    1. the largest component
    2. 3
    3. the magnitude r
    Correct choice
    the magnitude r
The position vector of P(x, y, z) has magnitude √(x² + y² + z²). Source: syllabus Maths Part II, Ch 10 Vector Algebra.

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Tap every statement true of the cross product

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Questions
  1. Items
    1. Text
      Its magnitude involves sin θ
      Matches the category
      Yes
    2. Text
      It is perpendicular to the plane of a and b
      Matches the category
      Yes
    3. Text
      a, b and it form a right handed system
      Matches the category
      Yes
    4. Text
      It is a scalar
      Matches the category
      No
    5. Text
      It uses cos θ
      Matches the category
      No
    Category
    True of a × b
The right-handed system is the part most often left out. Source: syllabus Maths Part II, Ch 10 Vector Algebra.

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