Allied Maths II Phy 20U3MAC1-P

If 𝑟⃗=𝑥𝑖⃗ +𝑦 𝑗⃗+𝑧 𝑘⃗⃗, then ∇∙𝑟⃗=______

(a) 1 (b) 0 (c) 3 (d) -1

• 1

• 0

• 3

• 3-1

If 𝑟⃗ = 𝑥𝑖⃗ +𝑦 𝑗⃗ +𝑧 𝑘⃗⃗, then ∇×𝑟⃗ =______

(a) 1 (b) 0 (c) 3 (d)-3

• 1

• 0

• 3

• -3

A vector function 𝐹⃗ is called solenoidal if_____

• 𝑑𝑖𝑣 𝐹⃗ = 0

• 𝑔𝑟𝑎𝑑 𝐹⃗ = 0

• 𝑐𝑢𝑟𝑙 𝐹⃗=0

A vector function 𝐹⃗ is called irrotational if______

• 𝑑𝑖𝑣 𝐹⃗ = 0

• 𝑔𝑟𝑎𝑑 𝐹⃗ = 0

• 𝑐𝑢𝑟𝑙 𝐹⃗=0

• None of the these

Unit normal to a surface Ø(𝑥,𝑦,𝑧) = 𝑐 is

(a) ∇∅|∇∅| (b) |∇∅| (c) |∇∅|2 (d) ∇∅

• ∇∅ / |∇∅|

• |∇∅|

• |∇∅|2

• ∇∅

A vector 𝑓⃗ is called a harmonic vector if ______

• ∇𝑓⃗ = 0

• ∇²𝑓⃗ = 0

• ∇² 𝑓⃗⃗⃗⃗ = 𝑓⃗

• None of the above