TS EAMCET · Maths · Vector Algebra
If \(\overrightarrow{\mathbf{a}}, \overrightarrow{\mathbf{b}}, \overrightarrow{\mathbf{c}}\) are three vectors such that \(\overrightarrow{\mathbf{a}}=\overrightarrow{\mathbf{b}}+\overrightarrow{\mathbf{c}}\) and the angle between \(\overrightarrow{\mathbf{b}}\) and \(\overrightarrow{\mathbf{c}}\) is \(\frac{\pi}{2}\), then:
- A \(a^2=b^2+c^2\)
- B \(b^2=c^2+a^2\)
- C \(c^2=a^2+b^2\)
- D \(2 a^2-b^2=c^2\)
Answer & Solution
Correct Answer
(A) \(a^2=b^2+c^2\)
Step-by-step Solution
Detailed explanation
Given that \(\overrightarrow{\mathbf{a}}=\overrightarrow{\mathbf{b}}+\overrightarrow{\mathbf{c}}\) and \(\overrightarrow{\mathbf{b}} \perp \overrightarrow{\mathbf{c}}\) then \((\overrightarrow{\mathbf{a}})^2=(\overrightarrow{\mathbf{b}})^2+(\overrightarrow{\mathbf{c}})^2\)…
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