3.18 Intersections and angles of lines and planes

3.18 Intersections and angles of lines and planes Quiz

IB Maths: Analysis and Approaches HL: Quiz

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  1. 1. How many points do the line r=k+t(i+j+k)\mathbf{r} = \mathbf{k} + t(\mathbf{i} + \mathbf{j} + \mathbf{k}) and the plane x+y−2z=5x + y - 2z = 5 have in common?

    • A. None
    • B. Exactly one
    • C. Exactly two
    • D. Infinitely many

  2. 2. Find the acute angle between the planes z=0z = 0 and x+z=3x + z = 3.

    • A. 30∘30^\circ
    • B. 45∘45^\circ
    • C. 60∘60^\circ
    • D. 90∘90^\circ

  3. 3. Which is a direction vector of the line of intersection of x+y=1x + y = 1 and y+z=2y + z = 2?

    • A. i+2j+k\mathbf{i} + 2\mathbf{j} + \mathbf{k}
    • B. i+j+k\mathbf{i} + \mathbf{j} + \mathbf{k}
    • C. i−j+k\mathbf{i} - \mathbf{j} + \mathbf{k}
    • D. j\mathbf{j}

  4. 4. Three planes have no two normals parallel, and the system of their equations has no solution. How are they arranged?

    • A. They meet at one point
    • B. They form a triangular prism
    • C. Two of them are parallel
    • D. They meet in a common line

  5. 5. Find the acute angle between the line with direction i+j+k\mathbf{i} + \mathbf{j} + \mathbf{k} and the plane z=0z = 0, to one decimal place.

    • A. 54.7∘54.7^\circ
    • B. 45.0∘45.0^\circ
    • C. 90.0∘90.0^\circ
    • D. 35.3∘35.3^\circ

Quiz