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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→.
Find all the vectors of magnitude 3√3 which are collinear to vector î + ĵ + k̂.
If a⃗, b⃗, c⃗ and d⃗ are four non-zero vectors such that a⃗ × b⃗ = c⃗ × d⃗ and a⃗ × c⃗ = 4b⃗ × d⃗, then show that (a⃗ − 2d⃗) is parallel to (2b⃗ − c⃗) where a⃗ ≠ 2d⃗, c⃗ ≠ 2b⃗.
If a→ and b→ are two vectors such that |a→ + b→| = |b→|, then prove that (a→ + 2b→) is perpendicular to a→.
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