JEE Mains · Maths · STD 12 - 10. vector algebra
Let \(\vec a = 3\hat i + 2\hat j + 2\hat k\) and \(\vec b = \hat i + 2\hat j - 2\hat k\) be two vectors. If a vector perpendicular to both the vectors \(\vec a + \vec b\) and \(\vec a - \vec b\) has the magnitude \(12\) then one such vector is
- A \(4\,\left( {2\hat i - 2\hat j - \hat k} \right)\)
- B \(4\,\left( {2\hat i - 2\hat j + \hat k} \right)\)
- C \(4\,\left( {2\hat i + 2\hat j + \hat k} \right)\)
- D \(4\,\left( {2\hat i + 2\hat j - \hat k} \right)\)
Answer & Solution
Correct Answer
(A) \(4\,\left( {2\hat i - 2\hat j - \hat k} \right)\)
Step-by-step Solution
Detailed explanation
\((\vec{a}+\vec{b}) \times(\vec{a}-\vec{b})\) \( = 2\left| {\begin{array}{*{20}{c}} {\hat i}&{\hat j}&{\hat k}\\ 1&2&{ - 2}\\ 3&2&2 \end{array}} \right|\) \(=2(8 \hat{i}-8 \hat{j}+4 \hat{k})\) \(\text { Required vector }=\pm 12 \frac{(2 \hat{i}-2 \hat{j}-\hat{k})}{3}\)…
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