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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 the direction cosines of a line are √3 k, √3 k, √3 k, then the value of k is :
Assertion (A) : A line in space cannot be drawn perpendicular to x, y and z axes simultaneously. Reason (R) : For any line making angles, α, β, γ with the positive directions of x, y and z axes respectively, cos² α + cos² β + cos² γ = 1.
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 ?
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