If a⃗ and b⃗ are two vectors such that |a⃗ + b⃗| = |b⃗|, then prove that (a⃗ + 2b⃗) is perpendicular to a⃗.

Question

TextScalar Product of Two VectorsProperties of Vector AdditionCBSE PYQ

Loading...

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: