Let be a unit vector satisfying

MATHEMATICS · Single correct · CBSE · Mathematics · Vector Algebra · Vector Algebra

Problem

Let r^\hat{\mathbf{r}} be a unit vector satisfying r^×a=b\hat{\mathbf{r}} \times \mathbf{a} = \mathbf{b} , where ∣a∣=3|\mathbf{a}| = \sqrt{3} and ∣b∣=2|\mathbf{b}| = \sqrt{2} . Then, (1) r^=23(a+a×b)\hat{\mathbf{r}} = \frac{2}{3}(\mathbf{a} + \mathbf{a} \times \mathbf{b}) (2) r^=13(a+a×b)\hat{\mathbf{r}} = \frac{1}{3}(\mathbf{a} + \mathbf{a} \times \mathbf{b}) (3) r^=23(−a+a×b)\hat{\mathbf{r}} = \frac{2}{3}(-\mathbf{a} + \mathbf{a} \times \mathbf{b}) (4) r^=13(−a+a×b)\hat{\mathbf{r}} = \frac{1}{3}(-\mathbf{a} + \mathbf{a} \times \mathbf{b})

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