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vectors lying on a plane?

All the vectors that lie to a plane are perpendicular to the normal vector to the plane.

Does it mean that these same vectors are parallel to each other?

Update:

Thanks for your answer.

But graphically speaking, they don’t seem to form a 90 degree angle with the normal vector. How can I visualise this in my mind?

2 Answers

Relevance
  • 3 months ago
    Favourite answer

    No.

    In 3D space, those vectors could be going in all sorts of directions and need not be parallel to each other.

    Look at the diagram below. The surface normal is blue. A subset of the perpendicular vectors in the plane are shown in black, but they aren't parallel to each other.

    UPDATE:

    I tried to add right angle symbols to the picture to show the vectors in the plane are all perpendicular to the normal. But you can see they all go in different directions, not parallel. 

    If it helps, just think of the 3 axes (x, y and z). The z-axis is perpendicular to the xy plane. It's also perpendicular to the x-axis and the y-axis. But the x-axis and the y-axis are *perpendicular* to each other, not parallel.

    UPDATE #2:

    Take a look at the second image I included as a link. You can see a circular staircase with a compass rose at its base. The pole is going up and down so it is perpendicular to the floor. Looking at the lines that radiate away from the pole, they are each at 90° to the pole. But they are obviously not parallel to each other.

    Attachment image
  • ?
    Lv 7
    3 months ago

    No.  Think of the plane vectors (a) parallel to the x-axis, (b) parallel to the y-axis, and (c) halfway in between, i.e., in the x-y plane but pointing towards 45 degrees.

    All of these vectors are perpendicular to the z-axis (which is the normal vector to the plane).  Yet the vectors in the paragraph above are not parallel to each other.

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