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Let $$\vec{a}=\hat{j}-\hat{k}$$ and$$\vec{c}=\hat{i}-\hat{j}-\hat{k}$$ . Then the vector $$\vec{b}$$ satisfying $$\vec{a} \times \vec{b}+\vec{c}=\overrightarrow{0} \ and \ \vec{a} . \vec{b}=3$$ is :

(1)$$-\hat{\mathrm{i}}+\hat{\mathrm{j}}-2 \hat{\mathrm{k}}$$

(2) $$2 \hat{\mathrm{i}}-\hat{\mathrm{j}}+2 \hat{\mathrm{k}}$$

(3)$$\hat{\mathrm{i}}-\hat{\mathrm{j}}-2 \hat{\mathrm{k}}$$

(4) $$\hat{\mathrm{i}}+\hat{\mathrm{j}}-2 \hat{\mathrm{k}}$$

from [AIEEE-2010]
in Vector | 9 views