If the component of vector along the direction of vector is zero, what can you conclude about these two vectors?

Question

Mathematics

Seth

7 September, 06:43

If the component of vector along the direction of vector is zero, what can you conclude about these two vectors?

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Eliezer Webb · Answer 1

The vectors are perpendicular

Step-by-step explanation:

Assuming two non-null vectors A and B, if the component of vector A along the direction of vector B is zero, then it can be concluded that the vectors are perpendicular.

For instance, let vector A be (x, 0). Any vector B of the form (0, y) is perpendicular to vector A. It is easy to note how the vectors are perpendicular in this example since their directions are along the x and y axis, but the property holds for any given pair of vectors.