Vector Analysis

Choose all the correct answers:

A vector A is a quantity which

• Has magnitude

• Has direction

• Adds according to the parallelogram law

• Is independent of the coordinate system

The dot product $\left(1,\ -2,\ 2\right)\cdot\left(-1,\ 1,\ 3\right)$ is equal to

• 0

• 3

• 9

• None of the above

A $\cdot$ B = 0 means that

• A and B are colinear

• A and B are parallel

• A and B are perpendicular

• None of the above 

A quantity that has both magnitude and direction is called a scalar quantity.

• True
• False

The dot product of two vectors is a scalar. The cross product of two vectors is a vector. State True/False.

• True

• False

A vector is said to be solenoidal when its

• a) Divergence is zero

• b) Divergence is unity

• c) Curl is zero

• d) Curl is unity

A field has zero divergence and it has curls. The field is said to be

• a) Divergent, rotational

• b) Solenoidal, rotational

• c) Solenoidal, irrotational

• d) Divergent, irrotational

The volume integral is three dimensional. State True/False

• True

• False

 $\nabla.\overrightarrow{\ r\ \ }\ =x\ \overline{i}\ +y\ \overline{i}\ +z\ \overline{k}$ ,  or  div $\overrightarrow{\ r\ }$  =

• 3

• 1

• 2

•  $\overrightarrow{\ r\ }$  

 $\int_A^B\overrightarrow{f\ }.d\ \overrightarrow{r\ }$  is,

• Volume integral

• Surface integral

• Line integral

• None of the above