Question

Assertion (A) : For two non-zero vectors a→ and b→, a→ · b→ = b→ · a→. Reason (R) : For two non-zero vectors a→ and b→, a→ × b→ = b→ × a→.

Let a→ and b→ be two non-zero vectors. Prove that |a→ × b→| ≤ |a→||b→|. State the condition under which equality holds, i.e., |a→ × b→| = |a→||b→|.

Let →a be any vector such that |→a| = a. The value of |→a × î|² + |→a × ĵ|² + |→a × k̂|² is:

Find a vector of magnitude 4 units perpendicular to each of the vectors 2î − ĵ + k̂ and î + ĵ − k̂ and hence verify your answer.