JEE Mains · Maths · STD 12 - 10. vector algebra
Let \(\vec{a}=\hat{i}+\hat{j}-\hat{k}\) and \(\vec{c}=2 \hat{i}-3 \hat{j}+2 \hat{k}\). Then the number of vectors \(\vec{b}\) such that \(\vec{b} \times \vec{c}=\vec{a}\) and \(|\vec{b}| \in\{1,2, \ldots ., 10\}\) is
- A \(3\)
- B \(1\)
- C \(2\)
- D \(0\)
Answer & Solution
Correct Answer
(D) \(0\)
Step-by-step Solution
Detailed explanation
\(\vec{a}=i+j-k\) \(\vec{c}=2 i-3 j+2 k\) \(\vec{b} \times \vec{c}=\vec{a}\) \(|\vec{b}| \in\{1,2 \ldots \ldots 10\}\) \(\because \vec{b} \times \vec{c}=\vec{a}\) \(\Rightarrow \vec{a}\) is perpendicular to \(\vec{b}\) as well as \(\vec{a}\) is perpendicular to \(\vec{C}\) Now…
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