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AP EAMCET · Maths · Vector Algebra

Let \(u\) and \(v\) be two vectors. Then \(|u-v|=|| u|-| v||\) if and only if

  1. A \(|u|=|v|\)
  2. B \(u\) and \(v\) have the same direction
  3. C \(u\) and \(v\) have the opposite direction
  4. D \(u=v\)
Verified Solution

Answer & Solution

Correct Answer

(B) \(u\) and \(v\) have the same direction

Step-by-step Solution

Detailed explanation

Since, \(|u-v|^2=|u|^2+|v|^2-2 \vec{u} \cdot \vec{v}\) and \(\| u|-| v||^2=|u|^2+|v|^2-2|\vec{u}||\vec{v}|\) Now, \(|u-v|^2=\left.|| u|-| v\right|^2\) only, when It only happens when \(u\) and \(v\) have same direction.…