M3(unit-1)

What is the divergence of the vector field f⃗ =3x2i^+5xy2j^+xyz3k^ at the point (1, 2, 3).

Divergence of f⃗ (x,y,z)=(xi^+yj^+zk^)(x2+y2+z2)3/2,(x,y,z)≠(0,0,0).

Curl of f⃗ (x,y,z)=2xyi^+(x2+z2)j^+2zyk^ is ________

Divergence of f⃗ (x,y,z)=exyi^−cosyj^+(sinz)2k^.

A vector field which has a vanishing divergence is called as ____________

Divergence and Curl of a vector field are ___________

A vector field with a vanishing curl is called as __________

The curl of vector field f⃗ (x,y,z)=x2i^+2zj^–yk^ is _________

• -3i^

• -3j^

• -3k^

• 0

Find the directional derivative of φ = xy² + yz³ at (1, -1, 1), towards the point (2, 1, -1).

The directional derivative of φ(x,y) at the point A(3,2) towards the point B(2,3). What is 32–√ and toward the point (1,0) is 8–√. What is the directional derivative at the point A towards the point D.

• 65

• 75√

• 65√

• 75