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AP Intermediate 2nd Year Vector Algebra and 3D Geometry — practice questions — page 3

Explore 218 free Vector Algebra and 3D Geometry questions in AP Intermediate 2nd Year 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 61–90 of 218.

The two productsRead the answer and worked solution →Complete the angle formulaRead the answer and worked solution →True or false: scalar multiplicationRead the answer and worked solution →Order the steps: build a unit vector from a pointRead the answer and worked solution →Match each law to what it saysRead the answer and worked solution →Which vectors are these?Read the answer and worked solution →True or false: vector vocabularyRead the answer and worked solution →Spot the one that does not belongRead 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 →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 →A quantity with magnitude as well as direction is a:Read the answer and worked solution →Which of these is a scalar quantity?Read the answer and worked solution →Which of these is a vector quantity?Read the answer and worked solution →A vector whose initial and terminal points coincide is the:Read the answer and worked solution →A vector of magnitude one is called a:Read the answer and worked solution →The distance between initial and terminal points is the vector's:Read the answer and worked solution →On a vector diagram, direction is shown by the: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 →

Worked practice questions

The two products

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Questions
  1. Question
    a · b equals
    Choices
    1. |a||b| sin θ
    2. |a| + |b|
    3. |a||b| cos θ
    Correct choice
    |a||b| cos θ
  2. Question
    The magnitude of a × b involves
    Choices
    1. sin θ
    2. cos θ
    3. tan θ
    Correct choice
    sin θ
  3. Question
    a × b points
    Choices
    1. along a
    2. perpendicular to both a and b
    3. along b
    Correct choice
    perpendicular to both a and b
  4. Question
    In component form a · b equals
    Choices
    1. a₁b₁ − a₂b₂ + a₃b₃
    2. a₁ + b₁
    3. a₁b₁ + a₂b₂ + a₃b₃
    Correct choice
    a₁b₁ + a₂b₂ + a₃b₃
Both products carry the same magnitudes only the trigonometric factor and the type of the answer differ. Source: syllabus Maths Part II, Ch 10 Vector Algebra.

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Complete the angle formula

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Missing parts
  1. Answer
    cos θ
    Choices
    1. cos θ
    2. sin θ
    3. tan θ
  2. Answer
    |a||b|
    Choices
    1. |a||b|
    2. |a| + |b|
    3. a · b
Complete the statement
The scalar product is defined as |a||b| times {0}. Rearranged, the angle between two vectors satisfies cos θ = (a · b) divided by {1}.
Rearranging the scalar product is how the chapter finds angles. Source: syllabus Maths Part II, Ch 10 Vector Algebra.

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True or false: scalar multiplication

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Questions
  1. Statement is true
    Yes
    Statement
    Multiplying a vector by λ changes its magnitude by |λ|.
  2. Statement is true
    Yes
    Statement
    A positive λ keeps the direction the same.
  3. Statement is true
    Yes
    Statement
    A negative λ reverses the direction.
  4. Statement is true
    No
    Statement
    Multiplying by a scalar turns a vector into a number.
  5. Statement is true
    Yes
    Statement
    Multiplying by λ = 1 leaves the vector unchanged.
Multiplying by λ scales the magnitude by |λ| and flips the direction only when λ is negative. Source: syllabus Maths Part II, Ch 10 Vector Algebra.

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