JEE Mains · Maths · STD 12 - 10. vector algebra
Let \(\vec{a}=6 \hat{i}+9 \hat{j}+12 \hat{k}, \vec{b}=\alpha \hat{i}+11 \hat{j}-2 \hat{k}\) and \(\vec{c}\) be vectors such that \(\vec{a} \times \vec{c}=\vec{a} \times \vec{b}\). If \(\vec{a} \cdot \vec{c}=-12\), \(\vec{c} .(\hat{i}-2 \hat{j}+\hat{k})=5\), then \(\vec{c} \cdot(\hat{i}+\hat{j}+\hat{k})\) is equal to \(.............\).
- A \(10\)
- B \(11\)
- C \(12\)
- D \(13\)
Answer & Solution
Correct Answer
(B) \(11\)
Step-by-step Solution
Detailed explanation
\(\overrightarrow{ a } \times \overrightarrow{ c }=\overrightarrow{ a } \times 5\) \(\Rightarrow \overrightarrow{ a } \times(\overrightarrow{ c }-\overrightarrow{ b })=0\) \(\vec{a} \|^{ I }(\overrightarrow{ c }-\overrightarrow{ b })\)…
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