If the dot product of two non-zero vectors vanishes, the vectors will be:

Explanation

If the dot product of two non-zero vectors vanishes, it means that the vectors are perpendicular to each other. This is the correct option (c). (a) If two vectors are parallel to each other, their dot product will not be zero. It will be equal to the product of their magnitudes. (b) If two vectors are anti-parallel to each other, their dot product will be negative. It will be equal to the negative product of their magnitudes. (c)When the dot product of two non-zero vectors vanishes, it means that the vectors are perpendicular to each other. In other words, the angle between the two vectors is 90 degrees. The dot product of two vectors A and B is calculated using the formula: A · B = |A| * |B| * cos(θ) where |A| and |B| are the magnitudes of vectors A and B, and θ (theta) is the angle between them. If the dot product is zero, it means that the cosine of the angle between the vectors is zero. And the only angle for which the cosine is zero is 90 degrees, which corresponds to the vectors being perpendicular to each other. So, when the dot product of two non-zero vectors is zero, it indicates that the vectors are indeed perpendicular to each other. (d) If the dot product of two non-zero vectors is zero, it means that they are perpendicular to each other. Therefore, option (d) is not correct. In summary, when the dot product of two non-zero vectors vanishes, it indicates that the vectors are perpendicular to each other.