The vector cross product (2i + 6j + 27k) × (i + pj + qk) = 0 implies that the two vectors are parallel. For the cross product to be zero, the components must satisfy the condition: 2p + 6q = 0.
This defines a relationship between p and q.

Class 12 Maths, Vector Algebra, Chapter 10 focuses on the study of vectors and their operations. It covers addition, subtraction, scalar and vector products, dot product, cross product, and their applications. Students learn to find the magnitude and direction of vectors, solve geometric problems and apply these concepts to real-life situations in various fields of science and engineering.