Let $\vec{OA} = 2\hat{i} - \hat{j} + \hat{k}$ and $\vec{OB} = \hat{i} + \hat{j} - \hat{k}$. Then

A. The magnitude of vector $\vec{OA}$ is 6

B. The magnitude of vector $\vec{OB}$ is $\sqrt{3}$

C. The vector $\vec{AB}$ is $(-\hat{i} + 2\hat{j} - 2\hat{k})$

D. $\vec{OA} \cdot \vec{OB} = 0$

E. $\vec{OA} \parallel \vec{OB}$

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The position vector of the point which divides the join of the points $2\vec{a}-3\vec{b}$ and $3\vec{a}-2\vec{b}$ externally in the ratio 2:3, is:

A unit vector perpendicular to both the vectors $4\hat{i}-\hat{j}+3\hat{k}$ and $-2\hat{i}+\hat{j}-2\hat{k}$ is:

If the points $A, B, C$ with position vectors $20\hat{i} + \lambda\hat{j}$, $5\hat{i} - \hat{j}$ and $10\hat{i} - 13\hat{j}$ respectively are collinear, then the value of $\lambda$ is

The position vector of a point which divides the line joining the points with position vectors $(\vec{a} - 2\vec{b})$ and $(2\vec{a} + \vec{b})$ externally in the ratio 2:1, is

If a unit vector $\hat a$ makes an angle $\dfrac{\pi}{3}$ with $\hat i$, $\dfrac{\pi}{4}$ with $\hat j$ and an acute angle $\theta$ with $\hat k$, then the respective value of $\theta$ and $\hat a$ are

Match List - I with List - II.

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