ExamBro
ExamBro
TS EAMCET · Maths · Vector Algebra

If \(\overrightarrow{\mathbf{u}}=\overrightarrow{\mathbf{a}}-\overrightarrow{\mathbf{b}}, \overrightarrow{\mathbf{v}}=\overrightarrow{\mathbf{a}}+\overrightarrow{\mathbf{b}},|\overrightarrow{\mathbf{a}}|=|\overrightarrow{\mathbf{b}}|=2\) then \(|\overrightarrow{\mathbf{u}} \times \overrightarrow{\mathbf{v}}|\) is equal to

  1. A \(2 \sqrt{16-(\overrightarrow{\mathbf{a}} \cdot \overrightarrow{\mathbf{b}})^2}\)
  2. B \(\sqrt{16-(\overrightarrow{\mathbf{a}} \cdot \overrightarrow{\mathbf{b}})^2}\)
  3. C \(2 \sqrt{4-(\overrightarrow{\mathbf{a}} \cdot \overrightarrow{\mathbf{b}})^2}\)
  4. D \(\sqrt{4-(\overrightarrow{\mathbf{a}} \cdot \overrightarrow{\mathbf{b}})^2}\)
Verified Solution

Answer & Solution

Correct Answer

(A) \(2 \sqrt{16-(\overrightarrow{\mathbf{a}} \cdot \overrightarrow{\mathbf{b}})^2}\)

Step-by-step Solution

Detailed explanation

We have, \(\overrightarrow{\mathbf{u}}=\overrightarrow{\mathbf{a}}-\overrightarrow{\mathbf{b}}, \overrightarrow{\mathbf{v}}=\overrightarrow{\mathbf{a}}+\overrightarrow{\mathbf{b}}\)…