MHT CET · Maths · Vector Algebra
Let \(\vec{a}, \vec{b}, \vec{c}\) be vectors of lengths \(3,4,5\) respectively. Let \(\vec{a}\) be perpendicular to \(\vec{b}+\vec{c}, \vec{b}\) be perpendicular to \(\vec{c}+\vec{a}\) and \(\vec{c}\) be perpendicular to \(\vec{a}+\vec{b}\), then the length of vector \(\vec{a}+\vec{b}+\vec{c}\) is
- A \(5\)
- B \(5 \sqrt{3}\)
- C \(5 \sqrt{2}\)
- D \(5 \sqrt{6}\)
Answer & Solution
Correct Answer
(C) \(5 \sqrt{2}\)
Step-by-step Solution
Detailed explanation
\(\text { Now }|\vec{a}+\vec{b}+\vec{c}|=\) \(\sqrt{|\vec{a}|^2+|\vec{b}|^2+|\vec{c}|^2+2 \vec{a} \cdot \vec{b}+2 \vec{b} \cdot \vec{c}+2 \vec{c} \cdot \vec{a}}\)
\(=\sqrt{3^2+4^2+5^2+0} \quad[\because|\vec{a}|=3,|\vec{b}|=4,|\vec{c}|=\) \(5 \text { given and from(iv) }\)
\(=\sqrt{50}\)
\(=5 \sqrt{2}\)
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