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If a⃗ and b⃗ are two non-zero vectors such that (a⃗ + b⃗) ⊥ a⃗ and (2a⃗ + b⃗) ⊥ b⃗, then prove that |b⃗| = √2 |a⃗|.
For any two vectors a→ and b→, which of the following statements is always true ?
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→.
If a→ and b→ are two vectors such that |a→ + b→| = |b→|, then prove that (a→ + 2b→) is perpendicular to a→.
If a⃗ and b⃗ are two vectors such that |a⃗ + b⃗| = |b⃗|, then prove that (a⃗ + 2b⃗) is perpendicular to a⃗.
If a⃗ and b⃗ are unit vectors and θ is the angle between them, then prove that sin(θ/2) = (1/2)|a⃗ - b⃗|.
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