The scalar product of two vectors is negative when they are:

Explanation

(a) Anti-parallel vectors: When two vectors are anti-parallel, it means they point in exactly opposite directions. In this case, the scalar product (or dot product) of the vectors is indeed negative. This happens because the dot product takes into account both the magnitudes and the cosine of the angle between the vectors. (b) Parallel vectors: When two vectors are parallel, meaning they point in the same direction, the scalar product is not negative. The scalar product of parallel vectors is positive or zero, depending on the angle between them. (c) Perpendicular vectors: When two vectors are perpendicular or orthogonal to each other, the scalar product is actually zero. It means there is no component of one vector in the direction of the other, resulting in a zero scalar product. (d) Parallel with some magnitude: This option is not correct. If two vectors are parallel and have the same magnitude, the scalar product is positive or zero, not negative. So, the correct option is (a). The scalar product of two vectors is negative when they are anti-parallel.