JEE Mains · Maths · STD 12 - 10. vector algebra
Let \(\vec a = 2\hat i + \hat j - 2\hat k\) and \(\vec b = \hat i + \hat j\) . Let \(\vec c\) be vector such that \(\left| {\vec c - \vec a} \right| = 3,\;\left| {\left( {\vec a \times \vec b} \right) \times \vec c} \right| = 3\) and the angle between \(\vec c\) and \(\vec a \times \vec b\) be \(30^\circ \) . Then \(\vec a \cdot \vec c\) is equal to :
- A \(\frac{1}{8}\)
- B \(\frac{{25}}{8}\)
- C \(2\)
- D \(5\)
Answer & Solution
Correct Answer
(C) \(2\)
Step-by-step Solution
Detailed explanation
\(\overrightarrow{\mathrm{a}}=2 \hat{\mathrm{i}}+\hat{\mathrm{j}}-2 \hat{\mathrm{k}}, \quad \overrightarrow{\mathrm{b}}=\hat{\mathrm{i}}+\hat{\mathrm{j}}\) \(\Rightarrow|\overrightarrow{\mathrm{a}}|=3\) \(\therefore \vec{a} \times \vec{b}=2 \hat{i}-2 \hat{j}+\hat{k}\)…
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