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ISC Class 12 Vector Algebra and 3D Geometry — practice questions — page 2

Explore 120 free Vector Algebra and 3D Geometry questions in ISC Class 12 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 31–60 of 120.

Order the steps: build a unit vector from a pointRead the answer and worked solution →Tap every statement true of the scalar productRead the answer and worked solution →Complete the definition of a unit vectorRead the answer and worked solution →The two productsRead the answer and worked solution →True or false: adding vectorsRead the answer and worked solution →Order the steps: find the angle between two vectorsRead the answer and worked solution →True or false: scalar multiplicationRead the answer and worked solution →True or false: the zero vectorRead the answer and worked solution →Assertion and reasonRead the answer and worked solution →Two are true, one is notRead 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 →Sort by what each formula gives youRead the answer and worked solution →Assertion and reason: productsRead the answer and worked solution →Complete the component-form rulesRead the answer and worked solution →Reading the vocabulary backRead the answer and worked solution →Complete the angle formulaRead the answer and worked solution →Which vectors are these?Read the answer and worked solution →True or false about vectorsRead the answer and worked solution →Scalar or vector?Read the answer and worked solution →Spot the odd one outRead the answer and worked solution →Match each vector termRead the answer and worked solution →The angle ϕ between a line with direction b and a plane with normal n satisfiesRead the answer and worked solution →The shortest distance between r = (1,2,3) + λ(2,3,4) and r = (2,4,5) + μ(3,4,5) isRead the answer and worked solution →Two non-zero vectors a and b are PERPENDICULAR if and only if:Read the answer and worked solution →If a = 2i + 3j + k and b = i − j + 2k, then a · b equals:Read the answer and worked solution →Reading the equationsRead the answer and worked solution →Same plane or different planes?Read the answer and worked solution →A line has direction ratios (1, 1, 2) and meets the plane x - y + z = 0. The angle ϕ between them satisfiesRead the answer and worked solution →If l, m, n are the direction cosines of a line in space, thenRead the answer and worked solution →

Worked practice questions

Order the steps: build a unit vector from a point

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Steps
  1. Write the position vector of the point from its coordinates
  2. Square each component and add the three squares
  3. Take the square root to get the magnitude
  4. Divide each component by that magnitude
  5. The result is the unit vector in the same direction
The route from coordinates to a unit vector, as the chapter sets it out. Source: syllabus Maths Part II, Ch 10 Vector Algebra.

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Tap every statement true of the scalar product

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Questions
  1. Items
    1. Text
      Written a · b
      Matches the category
      Yes
    2. Text
      Equals |a||b| cos θ
      Matches the category
      Yes
    3. Text
      Gives a number
      Matches the category
      Yes
    4. Text
      Gives a vector perpendicular to both
      Matches the category
      No
    5. Text
      Uses sin θ
      Matches the category
      No
    Category
    True of the SCALAR (dot) product
  2. Items
    1. Text
      Written a × b
      Matches the category
      Yes
    2. Text
      Uses sin θ
      Matches the category
      Yes
    3. Text
      Points perpendicular to the plane of a and b
      Matches the category
      Yes
    4. Text
      Gives a plain number
      Matches the category
      No
    5. Text
      Uses cos θ
      Matches the category
      No
    Category
    True of the CROSS product
The dot product is defined by |a||b| cos θ, and it is the tool for finding angles. Source: syllabus Maths Part II, Ch 10 Vector Algebra.

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Complete the definition of a unit vector

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Missing parts
  1. Answer
    1
    Choices
    1. 1
    2. 0
    3. any value
  2. Answer
    magnitude
    Choices
    1. magnitude
    2. direction
    3. components
Complete the statement
A unit vector has magnitude {0}. To build one in the direction of a vector a, divide a by its {1}.
Including how one is built from any given vector. Source: syllabus Maths Part II, Ch 10 Vector Algebra.

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