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AP Intermediate 2nd Year Vector Algebra and 3D Geometry — practice questions — page 6

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 151–180 of 218.

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 →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 →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 →The vector equation of a line passing through point a and parallel to vector b isRead the answer and worked solution →The equation of a plane through the intersection of π₁ = 0 and π₂ = 0 has the formRead the answer and worked solution →The line r = (2, -1, 4) + λ(3, 0, 2), expressed in symmetric Cartesian form, isRead the answer and worked solution →Spot the one that does not belongRead the answer and worked solution →The Cartesian equation (x-1)/2 = (y-2)/3 = (z-3)/4 representsRead the answer and worked solution →The angle θ between two lines with direction vectors b₁ and b₂ is given byRead the answer and worked solution →The distance of the point (x₀, y₀, z₀) from the plane ax + by + cz + d = 0 isRead the answer and worked solution →The shortest distance between skew lines r = a₁ + λb₁ and r = a₂ + μb₂ isRead the answer and worked solution →Two lines r = a₁ + λb₁ and r = a₂ + μb₂ are coplanar if and only ifRead the answer and worked solution →The equation of a plane passing through point (x₁, y₁, z₁) with normal vector (a, b, c) isRead the answer and worked solution →The angle between the lines with direction ratios (1, 2, 2) and (2, 1, 2) satisfiesRead the answer and worked solution →The equation of the plane through the points (1,0,0), (0,1,0), (0,0,1) isRead the answer and worked solution →The distance between the parallel planes 2x + y + 2z = 8 and 4x + 2y + 4z = 5 isRead the answer and worked solution →The foot of the perpendicular from origin to the plane 2x + 3y - 6z = 14 isRead the answer and worked solution →

Worked practice questions

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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Sort by what each formula gives you

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Items
  1. Item
    cos θ = (a · b) ÷ (|a||b|)
    Category
    An angle
  2. Item
    √(x² + y² + z²)
    Category
    A magnitude
  3. Item
    |a||b| sin θ
    Category
    A magnitude
  4. Item
    a + b
    Category
    A new vector
  5. Item
    a × b
    Category
    A new vector
Categories
  1. Item
    An angle
  2. Item
    A magnitude
  3. Item
    A new vector
Keeping the outputs straight is the whole trick of this chapter. Source: syllabus Maths Part II, Ch 10 Vector Algebra.

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Assertion and reason: products

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Questions
  1. Reason
    It is defined using cos θ, which can be isolated.
    Verdict
    Both are true; the reason explains the assertion.
    Assertion
    The scalar product can find the angle between two vectors.
  2. Reason
    It is defined along a unit vector normal to their plane.
    Verdict
    Both are true; the reason explains the assertion.
    Assertion
    a × b is perpendicular to both a and b.
  3. Reason
    The scalar product returns a number.
    Verdict
    Both are true; the reason does not explain the assertion.
    Assertion
    A vector can be scaled by a negative number.
Both halves can be true without one explaining the other. Source: syllabus Maths Part II, Ch 10 Vector Algebra.

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