JEE Mains · Maths · STD 12 - 10. vector algebra
Let \(\vec a = \hat i + \hat j + \hat k,\,\,\,\vec c = \hat j - \hat k\) and a vector \(\vec b\) be such that \(\vec a \times \vec b = \,\vec c\) and \(\vec a\, \cdot \,\vec b = \,3.\) Then \(\left| {\vec b} \right|\) equals?
- A \(\sqrt {\frac{{11}}{3}} \)
- B \(\frac{{\sqrt {11} }}{3}\)
- C \(\frac{{11}}{{\sqrt 3 }}\)
- D \(\frac {11}{3}\)
Answer & Solution
Correct Answer
(A) \(\sqrt {\frac{{11}}{3}} \)
Step-by-step Solution
Detailed explanation
\(\because \vec{a}=\hat{i}+\hat{j}+\hat{k} \Rightarrow|\vec{a}|=\sqrt{3}\) \(\vec{c}=\hat{j}-\hat{k} \Rightarrow(\text { Given })|\bar{c}| \sqrt{2}\) Now, \(\vec{a} \times \vec{b}=\vec{c}\) \(\Rightarrow|\vec{a}||\vec{b}| \sin \theta=|\vec{c}|\)…
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