Find the value of p for which the lines r→ = λî + (2λ + 1)ĵ + (3λ + 2)k̂ and r→ = î – 3μĵ + (pμ + 7)k̂ are perpendicular to each other and also intersect. Also, find the point of intersection of the given lines.

Scalar Product of Two Vectors, Vector Equation of a Line in Three Dimensions | PadhAiPro

Question

TextScalar Product of Two VectorsVector Equation of a Line in Three DimensionsCBSE PYQ

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 and →b are two vectors such that |→a| = 1, |→b| = 2 and →a · →b = √3, then the angle between 2→a and –→b is: