The vectors from origin to the points A and B are $\vec{a}=2\hat{i}-3\hat{j}+2\hat{k}$ and $\vec{b}=2\hat{i}+3\hat{j}+\hat{k}$ respectively, then the area (in Sq. unit) of triangle OAB is:

The area of the parallelogram determined by the vectors $\hat{i} + 2\hat{j} + 3\hat{k}$ and $3\hat{i} - 2\hat{j} + \hat{k}$ is

If $\vec a=\hat i+\hat j+2\hat k$ and $\vec b=2\hat i+\hat j+2\hat k$, then the unit vector in the direction of $2\vec a-\vec b$ is equal to :

Given that $\vec{a} = -3\hat{i} - 6\hat{j} + 4\hat{k}$, $\vec{b} = 9\hat{i} - λ\hat{j} - 12\hat{k}$. If $\vec{a} \times \vec{b} = \vec{0}$, then the value of λ is

If $\vec{a} = 3\hat{i} - 6\vec{j} + \hat{k}$ and $\vec{b} = 2\hat{i} - 4\vec{j} + \lambda\hat{k}$ are such that $\vec{a} \parallel \vec{b}$, then $3\lambda + 2 =$

Match List I with List II

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If $|\vec{a}| = \sqrt{26}, |\vec{b}| = 7, |\vec{a}\times\vec{b}| = 35$ and $\theta$ be the angle between $\vec{a}$ and $\vec{b}$ then

Match the LIST-I with LIST-II

Choose the correct answer from the options given below: