A unit vector perpendicular to the vectors $\hat{i} - \hat{j}$ and $\hat{i} + \hat{j}$ is

The value of $\lambda$ for which the vectors $3\hat{i}+6\hat{j}-\hat{k}$ and $-2\hat{i}+4\hat{j}-\lambda\hat{k}$ are perpendicular is

The value of $\hat{i} \cdot (\hat{k} \times \hat{j}) + \hat{j} \cdot (\hat{i} \times \hat{k}) + \hat{k} \cdot (\hat{j} \times \hat{i})$ is

If $\vec{a} = \hat{i} + \hat{k}$, $\vec{b} = \hat{j} - \hat{k}$ and $\vec{c} = \hat{i} + \hat{j} + \hat{k}$ such that $\vec{r} \times \vec{b} = \vec{c} \times \vec{b}$ and $\vec{r} \cdot \vec{a} = 0$, then $\vec{r}$ is:

If $\vec a = 4\hat i+5\hat j-\hat k, \vec b=\hat i-4\hat j+5\hat k$ and $\vec c=3\hat i+\hat j-\hat k$. If a vector $\vec d$ is perpendicular to both $\vec a$ and $\vec b$ and $\vec c.\vec d=21$, then unit vector along $\vec d$ is

If $\vec{a} = 2\hat{i} - 3\hat{j} + \hat{k}$ and $\vec{b} = 2\hat{i} + \hat{j} - \hat{k}$, then which of the following statements is/are correct?

(A) $\vec{a}$ and $\vec{b}$ are collinear

(B) $\vec{a}$ and $\vec{b}$ are perpendicular

(C) Angle between $\vec{a}$ and $\vec{b}$ is $\frac{\pi}{4}$

(D) $|\vec{a} + \vec{b}| = 2\sqrt{5}$

Choose the correct answer from the options given below:

Let $\vec{a}$ and $\vec{b}$ be any two vectors such that $\vec{a} = 2\hat{i} + \hat{j} + 3\hat{k}$ and $\vec{b} = 3\hat{i} + 5\hat{j} - 2\hat{k}$ then

Match the LIST-I with LIST-II

Choose the correct answer from the options given below: