jee-main 2022 Q77

jee-main · India · session2_25jul_shift2 Vectors Introduction & 2D Angle or Cosine Between Vectors

Let $\vec{a} = \hat{i} - \hat{j} + 2\hat{k}$ and let $\vec{b}$ be a vector such that $\vec{a} \times \vec{b} = 2\hat{i} - \hat{k}$ and $\vec{a} \cdot \vec{b} = 3$. Then the projection of $\vec{b}$ on the vector $\vec{a} - \vec{b}$ is:
(1) $\frac{2}{\sqrt{21}}$
(2) $2\sqrt{\frac{3}{7}}$
(3) $\frac{2}{3}\sqrt{\frac{7}{3}}$
(4) $\frac{2}{3}$

Let $\vec{a} = \hat{i} - \hat{j} + 2\hat{k}$ and let $\vec{b}$ be a vector such that $\vec{a} \times \vec{b} = 2\hat{i} - \hat{k}$ and $\vec{a} \cdot \vec{b} = 3$. Then the projection of $\vec{b}$ on the vector $\vec{a} - \vec{b}$ is:\\
(1) $\frac{2}{\sqrt{21}}$\\
(2) $2\sqrt{\frac{3}{7}}$\\
(3) $\frac{2}{3}\sqrt{\frac{7}{3}}$\\
(4) $\frac{2}{3}$

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