JEE Mains · Maths · STD 12 - 10. vector algebra
Let \(\vec{a}=\hat{i}-3 \hat{j}+7 \hat{k}, \vec{b}=2 \hat{i}-\hat{j}+\hat{k}\) and \(\vec{c}\) be a vector such that \((\vec{a}+2 \vec{b}) \times \vec{c}=3(\vec{c} \times \vec{a})\). If \(\overrightarrow{\mathrm{a}} \cdot \overrightarrow{\mathrm{c}}=130\), then \(\overrightarrow{\mathrm{b}} \cdot \overrightarrow{\mathrm{c}}\) is equal to ....................
- A \(25\)
- B \(46\)
- C \(35\)
- D \(30\)
Answer & Solution
Correct Answer
(D) \(30\)
Step-by-step Solution
Detailed explanation
\( (\overrightarrow{\mathrm{a}}+2 \overrightarrow{\mathrm{b}}) \times \overrightarrow{\mathrm{c}}=3(\overrightarrow{\mathrm{c}} \times \overrightarrow{\mathrm{a}}) \) \( (2 \overrightarrow{\mathrm{b}}+4 \overrightarrow{\mathrm{a}}) \times \overrightarrow{\mathrm{c}}=0 \)…
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