If |a| = 3, |b| = 5, |c| = 4 and a + b + c = 0, then find the value of (a · b + b · c + c · a).

Question

TextProperties of Scalar (Dot) ProductCBSE PYQ

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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 ?

Scalar Product of Two Vectors

Properties of Scalar (Dot) Product

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→.

If →a, →b, →c are three non-zero unequal vectors such that →a · →b = →a · →c, then find the angle between →a and →b - →c.

If θ is the angle between two vectors a→ and b→, then a→ · b→ ≥ 0 only when :

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