JEE Mains · Maths · STD 12 - 10. vector algebra
Let \(\vec a = 3\hat i + 2\hat j + x\hat k\) and \(\vec b = \hat i - \hat j + \hat k\), for some real \(x\). Then \(\left| {\vec a \times \vec b} \right| = r\) is possible if
- A \(r \geq 5\sqrt {\frac{3}{2}} \)
- B \(3\sqrt {\frac{3}{2}} < r < 5\sqrt {\frac{3}{2}} \)
- C \(\sqrt {\frac{3}{2}} < r \leq 3\sqrt {\frac{3}{2}} \)
- D \(0 < r \leq \sqrt {\frac{3}{2}} \)
Answer & Solution
Correct Answer
(A) \(r \geq 5\sqrt {\frac{3}{2}} \)
Step-by-step Solution
Detailed explanation
\(\vec a \times \vec b = \left| {\begin{array}{*{20}{c}} {\hat i}&{\hat j}&{\hat k}\\ 3&2&x\\ 1&{ - 1}&1 \end{array}} \right|\) \(=(2+x) \hat{i}-(3-x) \hat{j}-5 \hat{k}\)…
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