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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 →a, →b, →c are three non-zero unequal vectors such that →a · →b = →a · →c, then find the angle between →a and →b - →c.
If θ is the angle between two vectors a→ and b→, then a→ · b→ ≥ 0 only when :
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