Consider two non-zero vectors p and q.
Answer the following questions.
(i) State the relationship connecting the scalar product of two non-zero vectors, their magnitudes, and the angle between them.
(ii) Explain what can be concluded about the angle between p and q in each of the following cases:
(a) p⋅q>0,
(b) p⋅q<0,
(c) p⋅q=0.
(iii) Without calculating the actual measure of the angle, classify the angle between the vectors r=2i−j+4k and s=−3i+5j+2k as acute, obtuse or right-angled. Justify your answer.