3.17 Equations of a plane

3.17 Equations of a plane Quiz

IB Maths: Analysis and Approaches HL: Quiz

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5 questions, one answer each

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  1. 1. Which vector is normal to the plane 3x−2y+z=73x - 2y + z = 7?

    • A. 3i+2j+k3\mathbf{i} + 2\mathbf{j} + \mathbf{k}
    • B. 3i−2j+k3\mathbf{i} - 2\mathbf{j} + \mathbf{k}
    • C. 7k7\mathbf{k}
    • D. i−2j+3k\mathbf{i} - 2\mathbf{j} + 3\mathbf{k}

  2. 2. Find the Cartesian equation of the plane through (2,0,3)(2, 0, 3) with normal i−j+k\mathbf{i} - \mathbf{j} + \mathbf{k}.

    • A. x−y+z=5x - y + z = 5
    • B. x−y+z=0x - y + z = 0
    • C. 2x+3z=12x + 3z = 1
    • D. x−y+z=−1x - y + z = -1

  3. 3. The plane through the origin contains the vectors i+j\mathbf{i} + \mathbf{j} and j+k\mathbf{j} + \mathbf{k}. What is its Cartesian equation?

    • A. x+y+z=0x + y + z = 0
    • B. x+2y+z=0x + 2y + z = 0
    • C. x−y+z=0x - y + z = 0
    • D. x−y+z=1x - y + z = 1

  4. 4. Which plane is parallel to, but different from, 2x−y+3z=42x - y + 3z = 4?

    • A. 4x−2y+6z=84x - 2y + 6z = 8
    • B. 2x+y+3z=42x + y + 3z = 4
    • C. x−y+z=4x - y + z = 4
    • D. −4x+2y−6z=1-4x + 2y - 6z = 1

  5. 5. Which vector lies in (is parallel to) the plane x+2y−z=4x + 2y - z = 4?

    • A. i+2j−k\mathbf{i} + 2\mathbf{j} - \mathbf{k}
    • B. 2i−j2\mathbf{i} - \mathbf{j}
    • C. i+j+k\mathbf{i} + \mathbf{j} + \mathbf{k}
    • D. j+k\mathbf{j} + \mathbf{k}

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