Three vectors A, B, and C add up to zero.
Question:

Three vectors A, B, and C add up to zero. Find which is false

(a) vector (A×B)C is not zero unless vectors B, C are parallel

(d) vector (A×B).C is not zero unless vectors B, C are parallel

(c) if vectors A, B, C define a plane, (A×B)C is in that plane

(d) (A×B).C = $|A||B||C|$ such that $\mathrm{C}^{2}=\mathrm{A}^{2}+\mathrm{B}^{2}$

Solution:

The correct answer is c) if vectors A, B, C define a plane, $(A \times B) C$ is in that plane and d) $(A \times B) . C=$ $|A \| B||C|$ such that $\mathrm{C}^{2}=\mathrm{A}^{2}+\mathrm{B}^{2}$