Physics · Scalars and Vectors

The dot product of two vectors A and B is given by A.B = |A||B| cosθ. If the angle θ between the vectors is 0°, cosθ = 1, so a vector dotted with itself (i.i, j.j, k.k) is 1, due to the unit magnitude of the vectors. If θ is 90°, cosθ = 0, so the dot product of two perpendicular vectors (i.j, j.k, k.i) is 0. Therefore, the correct answer is 1 for i.i = j.j = k.k, and 0 for i.j = j.k = k.i. The other options are incorrect as they do not accurately reflect these properties of the dot product for unit vectors.

This option is incorrect because the dot product of a unit vector with itself is always 1, not 0.

This is the correct answer because the dot product of a unit vector with itself (e.g., i.i) is 1. The dot product of two different perpendicular unit vectors (e.g., i.j) is 0.

This option is incorrect because the dot product of a unit vector with itself is not 0; it is 1.

This option is incorrect because the dot product of two different perpendicular unit vectors is 0, not 1.