Planes and the scalar product

Planes and the scalar product Quiz

Spec 6.2–4 · Edexcel A-Level Further Maths: Quiz

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5 questions, one answer each

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  1. 1. Find a⋅b\mathbf a\cdot\mathbf b for a=(1,2,−1)\mathbf a=(1,2,-1) and b=(3,0,4)\mathbf b=(3,0,4).

    • A. 77
    • B. 11
    • C. −1-1
    • D. −7-7

  2. 2. Write down a normal to the plane 2x−3y+z=52x-3y+z=5.

    • A. (2,−3,1)(2,-3,1)
    • B. (2,3,1)(2,3,1)
    • C. (5,5,5)(5,5,5)
    • D. (−2,−3,−1)(-2,-3,-1)

  3. 3. Find the Cartesian equation of the plane through (1,2,1)(1,2,1) with normal (2,−1,3)(2,-1,3).

    • A. 2x−y+3z=42x-y+3z=4
    • B. 2x−y+3z=02x-y+3z=0
    • C. 2x−y+3z=62x-y+3z=6
    • D. 2x−y+3z=32x-y+3z=3

  4. 4. To find the acute angle between two planes you use:

    • A. the direction vectors in the planes
    • B. the acute angle between their normal vectors
    • C. 90∘90^\circ minus the angle between the normals
    • D. the position vectors of points on them

  5. 5. Which vector is perpendicular to (2,1,−3)(2,1,-3)?

    • A. (2,1,3)(2,1,3)
    • B. (1,−2,−1)(1,-2,-1)
    • C. (1,1,1)(1,1,1)
    • D. (3,−1,2)(3,-1,2)

Quiz