Angles between planes and between lines and planes

Angles between planes and between lines and planes Quiz

Spec F3 · AQA A-Level Further Maths: Quiz

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  1. 1. Find the angle between the planes x+2y+2z=1x+2y+2z=1 and 2x+y−2z=32x+y-2z=3.

    • A. 0∘0^\circ
    • B. 45∘45^\circ
    • C. 90∘90^\circ
    • D. 60∘60^\circ

  2. 2. Find the angle between the line with direction (1,2,2)(1,2,2) and the plane z=0z=0.

    • A. 48.2∘48.2^\circ
    • B. 41.8∘41.8^\circ
    • C. 63.6∘63.6^\circ
    • D. 70.5∘70.5^\circ

  3. 3. Which expression gives the acute angle θ\theta between a line (direction b\mathbf b) and a plane (normal n\mathbf n)?

    • A. cos⁡θ=∣b⋅n∣∣b∣∣n∣\cos\theta=\frac{|\mathbf b\cdot\mathbf n|}{|\mathbf b||\mathbf n|}
    • B. tan⁡θ=∣b⋅n∣∣b∣∣n∣\tan\theta=\frac{|\mathbf b\cdot\mathbf n|}{|\mathbf b||\mathbf n|}
    • C. sin⁡θ=b⋅n∣b∣+∣n∣\sin\theta=\frac{\mathbf b\cdot\mathbf n}{|\mathbf b|+|\mathbf n|}
    • D. sin⁡θ=∣b⋅n∣∣b∣∣n∣\sin\theta=\frac{|\mathbf b\cdot\mathbf n|}{|\mathbf b||\mathbf n|}

  4. 4. Find the acute angle between the planes x+y+z=1x+y+z=1 and z=0z=0.

    • A. 54.7∘54.7^\circ
    • B. 35.3∘35.3^\circ
    • C. 45∘45^\circ
    • D. 90∘90^\circ

  5. 5. Two planes have n1⋅n2=−3\mathbf n_1\cdot\mathbf n_2=-3 and ∣n1∣∣n2∣=6|\mathbf n_1||\mathbf n_2|=6. What is the acute angle between them?

    • A. 120∘120^\circ
    • B. 60∘60^\circ
    • C. 30∘30^\circ
    • D. 150∘150^\circ

Quiz