JEE Mains · Maths · STD 12 - 10. vector algebra
Let \(\overrightarrow{\mathrm{a}}, \overrightarrow{\mathrm{b}}\) and \(\overrightarrow{\mathrm{c}}\) be three unit vectors such that \(|\vec{a}-\vec{b}|^{2}+|\vec{a}-\vec{c}|^{2}=8\) Then \(|\vec{a}+2 \vec{b}|^{2}+|\vec{a}+2 \vec{c}|^{2}\) is equal to
- A \(1\)
- B \(2\)
- C \(4\)
- D \(6\)
Answer & Solution
Correct Answer
(B) \(2\)
Step-by-step Solution
Detailed explanation
\(|\vec{a}|=|\vec{b}|=|\vec{c}|=1\) \(|\vec{a}-\vec{b}|^{2}+|\vec{a}-\vec{b}|^{2}=8\) \(\Rightarrow \quad|\vec{a}|^{2}+|\vec{b}|^{2}-2 \vec{a} \cdot \vec{b}+|\vec{a}|^{2}+|\vec{c}|^{2}-2 \vec{a} \cdot \vec{c}=8\)…
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