Show that the vectors 3î + ĵ – 2k̂, 2î – ĵ – 8k̂ and 4î – 2ĵ – 7k̂ form the vertices of a right triangle.

Question

TextScalar Product of Two VectorsMagnitude and Direction of a VectorCBSE PYQ

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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|.

Scalar Product of Two Vectors

Properties of Scalar (Dot) Product

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.

If |a→| = 2 and – 3 ≤ k ≤ 2, then |ka→| ∈ :