If a = b + c, then is it true that |a| = |b| + |c|? Justify your answer.

Question

TextProperties of Vector Addition

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

If a⃗ and b⃗ are unit vectors and θ is the angle between them, then prove that sin(θ/2) = (1/2)|a⃗ - b⃗|.

Scalar Product of Two Vectors

Properties of Vector Addition

(b) If a→, b→ and c→ are unit vectors, then prove that |a→ – b→|² + |b→ – c→|² + |c→ – a→|² ≤ 9.

For any two vectors a and b, we always have |a + b| ≤ |a| + |b| (triangle inequality).