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.

Question

CASE_STUDIESPosition and Displacement VectorsScalar Product of Two VectorsCBSE PYQ3 sub-questions

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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 :

The vector with terminal point A (2, – 3, 5) and initial point B (3, – 4, 7) is :

Position and Displacement Vectors

Components of a Vector

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.