If $a + b + c = 0$,then $a \times b$ is equal to:

If $|\hat{a} \cdot \hat{b}| = \frac{1}{2}$,then $|\hat{a} - \hat{b}|$ may be $:-$

The vectors from the origin to the points $A$ and $B$ are $\overrightarrow A = 3\hat i - 6\hat j + 2\hat k$ and $\overrightarrow B = 2\hat i + \hat j - 2\hat k$ respectively. The area of the triangle $OAB$ is:

If two vectors $\vec{A} = 4\hat{i} + n\hat{j} + 2\hat{k}$ and $\vec{B} = 2\hat{i} + 2\hat{j} - \hat{k}$ are mutually perpendicular to each other, then the value of '$n$' is:

If $\vec{P} = b \hat{i} + 6 \hat{j} + \hat{k}$ and $\vec{Q} = \hat{i} - a \hat{j} + 4 \hat{k}$ are perpendicular to each other,and $3b - a = 5$,find the values of $a$ and $b$.

In a right-handed Cartesian coordinate system (often referred to as a clockwise system when viewed from the positive axis),which of the following vector relations is correct?