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

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 1–30 of 120.

Spot the one that does not belongRead the answer and worked solution →Match each kind of vector to its definitionRead the answer and worked solution →True or false: vector vocabularyRead the answer and worked solution →Order the steps: angle between two lines from direction ratiosRead the answer and worked solution →Which of these is a vector quantity?Read the answer and worked solution →A plane meets the axes at (a,0,0), (0,b,0), (0,0,c). Its equation isRead the answer and worked solution →The girl's net movement from A to C is represented by a:Read the answer and worked solution →Tap the vector quantitiesRead the answer and worked solution →Scalar or vector, quicklyRead the answer and worked solution →Three vectors $\vec a, \vec b, \vec c$ are coplanar if and only if:Read the answer and worked solution →A quantity with magnitude as well as direction is a:Read the answer and worked solution →The distance between initial and terminal points is the vector's:Read the answer and worked solution →Does this produce a number or a vector?Read the answer and worked solution →A vector whose initial and terminal points coincide is the:Read the answer and worked solution →On a vector diagram, direction is shown by the:Read the answer and worked solution →Complete the vector definitionRead the answer and worked solution →Vector algebra bingoRead the answer and worked solution →Match the vector termRead the answer and worked solution →Match each law to what it saysRead the answer and worked solution →A vector of magnitude one is called a:Read the answer and worked solution →The unit vector along a given vector is written with which symbol?Read the answer and worked solution →Adding vectors by completing a parallelogram is the:Read the answer and worked solution →Vector addition where order does not matter is called:Read the answer and worked solution →The vectors i, j and k each have magnitude:Read the answer and worked solution →The vectors i, j and k lie along which axes?Read the answer and worked solution →A vector joining two points is found by applying the:Read the answer and worked solution →A directed line segment has magnitude and:Read the answer and worked solution →Where does a vector start, in the standard naming?Read the answer and worked solution →Which quantity in this list is NOT a vector?Read the answer and worked solution →A unit vector is mainly used to show a vector's:Read the answer and worked solution →

Worked practice questions

Spot the one that does not belong

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Questions
  1. Items
    1. a · b
    2. |a||b| cos θ
    3. a × b
    Odd item
    a × b
  2. Items
    1. Unit vector
    2. Zero vector
    3. Null vector
    Odd item
    Unit vector
  3. Items
    1. Coinitial
    2. Perpendicular
    3. Collinear
    Odd item
    Perpendicular
  4. Items
    1. î
    2. λ
    3. ĵ
    4. k̂
    Odd item
    λ
Grouped by which summary bullet each belongs to. Source: syllabus Maths Part II, Ch 10 Vector Algebra.

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Match each kind of vector to its definition

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Matching pairs
  1. Left
    Zero vector
    Right
    initial and terminal points coincide
  2. Left
    Unit vector
    Right
    magnitude is exactly 1
  3. Left
    Coinitial vectors
    Right
    share the same initial point
The six definitions your syllabus gives at the start of the chapter. Source: syllabus Maths Part II, Ch 10 Vector Algebra.

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True or false: vector vocabulary

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Questions
  1. Statement is true
    Yes
    Statement
    Coinitial vectors share the same initial point.
  2. Statement is true
    No
    Statement
    Collinear vectors must have the same magnitude.
  3. Statement is true
    Yes
    Statement
    Equal vectors have the same magnitude and direction.
  4. Statement is true
    No
    Statement
    The negative of a vector has the same direction.
  5. Statement is true
    Yes
    Statement
    The negative of a vector has the same magnitude.
The definitions are close together and get swapped constantly. Source: syllabus Maths Part II, Ch 10 Vector Algebra.

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