Assertion (A) : The vectors a⃗ = 6î + 2ĵ − 8k̂, b⃗ = 10î − 2ĵ − 6k̂ and c⃗ = 4î − 4ĵ + 2k̂ represent the sides of a right angled triangle. Reason (R) : Three non-zero vectors of which none of two are collinear forms a triangle if their resultant is zero vector or sum of any two vectors is equal to the third.

Triangle Law of Vector Addition, Scalar Product of Two Vectors, Components of a Vector | PadhAiPro

Question

Assertion-ReasonTriangle Law of Vector AdditionScalar Product of Two VectorsComponents of a VectorCBSE 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 :

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.