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Let θ be the angle between two unit vectors â and b̂ such that sin θ = 3/5. Then, â . b̂ is equal to :
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→.
The position vectors of vertices of △ ABC are A(2î – ĵ + k̂), B(î – 3ĵ – 5k̂) and C(3î – 4ĵ – 4k̂). Find all the angles of △ ABC.
An instructor at the astronomical centre shows three among the brightest stars in a particular constellation. Assume that the telescope is located at O(0, 0, 0) and the three stars have their locations at the points D, A and V having position vectors 2î + 3ĵ + 4k̂, 7î + 5ĵ + 8k̂ and –3î + 7ĵ + 11k̂ respectively.
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