Scalar product and perpendicular vectors

Scalar product and perpendicular vectors Quiz

Spec F3–F4 · AQA 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 when a=(1,2,3)\mathbf a=(1,2,3) and b=(4,−5,6)\mathbf b=(4,-5,6).

    • A. (4,−10,18)(4,-10,18)
    • B. −12-12
    • C. 1212
    • D. 3232

  2. 2. Find kk if (3,k,−2)(3,k,-2) is perpendicular to (2,−4,1)(2,-4,1).

    • A. −1-1
    • B. 11
    • C. 33
    • D. −3-3

  3. 3. Find the angle between (1,0,0)(1,0,0) and (1,1,0)(1,1,0).

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

  4. 4. Lines with direction vectors (1,2,2)(1,2,2) and (2,3,6)(2,3,6). Find the angle between the lines.

    • A. 72.2∘72.2^\circ
    • B. 162.2∘162.2^\circ
    • C. 45.0∘45.0^\circ
    • D. 17.8∘17.8^\circ

  5. 5. If a⋅b=0\mathbf a\cdot\mathbf b=0 and a\mathbf a, b\mathbf b are non-zero vectors, then

    • A. a\mathbf a and b\mathbf b are parallel
    • B. a=b\mathbf a=\mathbf b
    • C. a\mathbf a and b\mathbf b are perpendicular
    • D. ∣a∣=∣b∣|\mathbf a|=|\mathbf b|

Quiz