Vector Calculus Gradient

 $\overrightarrow{\ a\ }\ and\ \overrightarrow{\ b\ }\ are\ two\ non\ zero\ vectors\ then\ \left(\overrightarrow{\ a\ }\ \times\overrightarrow{\ b\ }\ \right)\ is\$  

• Parallel to  $\overrightarrow{\ a\ }$  

• Parallel to  $\overrightarrow{b\ }$  

• Perpendicular to  $\overrightarrow{\ a\ .}\overrightarrow{\ b\ }$  

• Perpendicular to  $\overrightarrow{\ a\ }$  

 $i\times\left(\overrightarrow{\ a\ }\times i\right)+j\times\left(\overrightarrow{\ a\ }\times j\right)+k\times\left(\overrightarrow{\ a\ }\times k\right)=$  

• 0

•  $\overrightarrow{\ a\ }$  

•  $2\overrightarrow{\ a\ }$  

• 3

The magnitude of vector  $\cos\theta\ i+\sin\theta\ j+k$  is

• 2

•  $\sqrt{2}$   

• 3

• 1

Tags

CCSS.HSN.VM.A.1

 $\nabla.\overrightarrow{\ r\ \ }\ =$ ,  or  div $\overrightarrow{\ r\ }$  =

• 3

• 1

• 2

•  $\overrightarrow{\ r\ }$  

 $\nabla^2\psi\left(x,y,z\right)=0,\$  the function  $\psi$  is

• Solenoidal

• Irrotational

• Harmonic

• None of the above

 $r=\left|\overrightarrow{\ r\ }\right|,\overrightarrow{\ r\ }=xi+yj+zk,\ then\ \Delta r=$  

•  $r^2$  

•  $\overrightarrow{\ r\ }$  

•  $r^3$  

•  $\frac{\overrightarrow{\ r\ }}{r}$  

Tags

CCSS.HSN.VM.A.1

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

• Volume integral

• Surface integral

• Line integral

• None of the above

 $x=3t^2,\ y=t^2-2t,\ z=t^3$  ,A particle moves along the given above curves. the magnitude of velocity at t=1, is

•  $3\sqrt{5}$  

•  $\sqrt{42}$  

•  $\sqrt{45}$  

•  $\sqrt{63}$  

 $\nabla\cdot\left(\nabla\times\overrightarrow{F}\right)$  
What will this operation result in?

• Scalar function

• Vector function

• Undefined

•  $\overrightarrow{\ F\ }$  

 $\nabla\times\left(\nabla\cdot\overrightarrow{F}\right)$  
What will this operation result in?

• Scalar function

• Vector function

• Undefined