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Further maths vector lines

Quiz by Callum Craven

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13 questions
Show answers
  • Q1
    What is the direction vector of the line passing through the points A(2, -1, 3) and B(5, 2, -4)?
    {'-3, 3, -7'}
    {'-3, -3, 7'}
    {'3, 3, -7'}
    {'3, -3, 7'}
    30s
  • Q2
    Which of the following is NOT a property of vectors in a 3D space?
    'Magnitude'
    'Scalar multiplication'
    'Length'
    'Direction'
    30s
  • Q3
    Which of the following is an equation for the line in 3D space passing through the point P(1, 2, -3) with direction vector <2, -1, 4>?
    'r = <1, 2, -3> + t<2, 1, -4>'
    'r = <1, 2, -3> + t<-2, 1, -4>'
    'r = <1, 2, -3> + t<2, -1, 4>'
    'r = <1, 2, -3> - t<2, -1, 4>'
    30s
  • Q4
    Given two vectors u = <2, -3, 1> and v = <1, 4, -2>, what is the dot product u · v?
    -11
    14
    -8
    4
    30s
  • Q5
    In 2D space, if two vector lines are parallel, what can be said about their direction vectors?
    Their direction vectors are equal
    Their direction vectors are proportional
    Their direction vectors are perpendicular
    Their direction vectors have no relation
    30s
  • Q6
    In 2D space, what is the magnitude of a vector?
    The length of the vector
    The direction of the vector
    The sum of its components
    The product of its components
    30s
  • Q7
    In 2D space, what is the dot product of two vectors?
    The difference of their magnitudes
    The product of their magnitudes and the cosine of the angle between them
    The product of their magnitudes
    The sum of their components
    30s
  • Q8
    If two vectors in 2D space are orthogonal, what can be said about their dot product?
    Their dot product is one
    Their dot product is undefined
    Their dot product is zero
    Their dot product is negative
    30s
  • Q9
    What is the dot product of two vectors?
    A scalar
    A matrix
    A vector
    An imaginary number
    30s
  • Q10
    What is the formula to calculate the distance between two points in 3D space?
    sqrt((x2-x1)^2 + (y2-y1)^2 + (z2-z1)^2)
    sqrt((x2+x1)^2 + (y2+y1)^2 + (z2+z1)^2)
    sqrt((x2-x1)^2 - (y2-y1)^2 + (z2-z1)^2)
    sqrt((x2-x1)^2 + (y2-y1)^2 + (z2+z1)^2)
    30s
  • Q11
    What is the equation of a plane in 3D space?
    Ax = By = Cz = D
    Ax + By = Cz + D
    Ax + By + Cz + D = 0
    Ax + By + Cz = D
    30s
  • Q12
    What is the formula to find the angle between two vectors in 3D space?
    tan⁡(θ) = (A⋅B) / (|A||B|)
    sin⁡(θ) = (A⋅B) / (|A||B|)
    cos⁡(θ) = (A⋅B) / (|A||B|)
    θ = (A⋅B) / (|A||B|)
    30s
  • Q13
    What is the formula to find the magnitude of a 2D vector?
    x + y
    (x + y)^2
    sqrt(x^2 + y^2)
    x - y
    30s

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