AP 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
- A \(2 \sqrt{16-(\overrightarrow{\mathbf{a}} \cdot \overrightarrow{\mathbf{b}})^2}\)
- B \(\sqrt{16-(\overrightarrow{\mathbf{a}} \cdot \overrightarrow{\mathbf{b}})^2}\)
- C \(2 \sqrt{4-(\overrightarrow{\mathbf{a}} \cdot \overrightarrow{\mathbf{b}})^2}\)
- D \(\sqrt{4-(\overrightarrow{\mathbf{a}} \cdot \overrightarrow{\mathbf{b}})^2}\)
Answer & Solution
Correct Answer
(A) \(2 \sqrt{16-(\overrightarrow{\mathbf{a}} \cdot \overrightarrow{\mathbf{b}})^2}\)
Step-by-step Solution
Detailed explanation
We have, \(\overrightarrow{\mathbf{u}}=\overrightarrow{\mathbf{a}}-\overrightarrow{\mathbf{b}}, \overrightarrow{\mathbf{v}}=\overrightarrow{\mathbf{a}}+\overrightarrow{\mathbf{b}}\)…
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