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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|.
In the given figure, ABCD is a parallelogram. If AB⃗ = 2î – 4ĵ + 5k̂ and DB⃗ = 3î – 6ĵ + 2k̂, then find AD⃗ and hence find the area of parallelogram ABCD.
For any two vectors a→ and b→, which of the following statements is always true ?
The unit vector perpendicular to both vectors î + k̂ and î – k̂ is :
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→.
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