JEE Mains · Maths · STD 12 - 10. vector algebra
Let \(\vec{a}=\hat{i}+\alpha \hat{j}+3 \hat{k}\) and \(\vec{b}=3 \hat{i}-\alpha \hat{j}+\hat{k} \cdot\) If the area of the parallelogram whose adjacent sides are represented by the vectors \(\vec{a}\) and \(\vec{b}\) is \(8 \sqrt{3}\) square units, then \(\overrightarrow{ a } \cdot \overrightarrow{ b }\) is equal to ....... .
- A \(10\)
- B \(2\)
- C \(5\)
- D \(4\)
Answer & Solution
Correct Answer
(B) \(2\)
Step-by-step Solution
Detailed explanation
\(\overrightarrow{ a }=\hat{ i }+\alpha \hat{ j }+3 \hat{ k }\) \(\overrightarrow{ b }=3 \hat{ i }-\alpha \hat{ j }+\hat{ k }\) area of parallelogram \(=|\overrightarrow{ a } \times \overrightarrow{ b }|=8 \sqrt{3}\).…
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