AP EAMCET · Maths · Vector Algebra
\(\mathbf{a}, \mathbf{b}\) are two vectors such that \(|\mathbf{a}|=\sqrt{3},|\mathbf{b}|=\sqrt{2}\). If \(\mathbf{x}\) is unit vector satisfying \(\mathbf{x} \times \mathbf{a}=\mathbf{b}\), then \(\mathbf{x}=\)
- A \(\frac{1}{2}[(x \cdot a) a-b \times a]\)
- B \(\frac{1}{2}[ \pm(x \cdot a) a+(b \times a)]\)
- C \(\frac{1}{2}[(x \cdot a) a+b \times a]\)
- D \(-8 \hat{i}-12 \hat{i}+24 \hat{k}\)
Answer & Solution
Correct Answer
(D) \(-8 \hat{i}-12 \hat{i}+24 \hat{k}\)
Step-by-step Solution
Detailed explanation
\begin{aligned} & \mathbf{a} \times(\mathbf{x} \times \mathbf{a})=\mathbf{a} \times \mathbf{b} \\ \Rightarrow & (\mathbf{a} \cdot \mathbf{a}) \mathbf{x}-(\mathbf{a} \cdot \mathbf{x}) \mathbf{a}=\mathbf{a} \times \mathbf{b}…
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