Vector Calculus Answers

Given that ∇f ( X, Y, Z) = 2XYZ^3ˆi +X^2Z^3ˆj + 3X^2YZ^2kˆ and f (1, − 2, 2) = 4 show that
f ( X, Y, Z) =X^2YZ^3 + 20 .

Evaluate ∫∫ A .nˆ dS , where A = x (cos)^2 y ˆi + xz ˆj + z (sin)^2y kˆ , over the surface of a sphere
with its centre at the origin and radius of 4 units.
note ^i=icap(unit vector) so on for other

A boat sails 3 km South, then 10 km Southeast. Use trigonometry to find the boat's distance and bearing from its starting point.

the displacement of a boat relative to water is represented by (3t)i+4(t2-1)j(read as 4 (t square-1)j) and that of water relative to ground is i-(et)j (read as i-(e power t)j).what is the velocity of the boat relative to ground if i&j represent 1km/hour east and north respectively?

If U = I + 3j - 2k and V = 4i - 2j - 4k are vectors, find 3U + V

Find the angle (in degrees) between the longest edge and the longest diagonal of a 2 by 5 by 6 rectangular box.

State and prove De Moivre’s Theorem

Given two vector A = 5i, B = 3j. Direction of (B x A) is ?

find the divergence A at point(2,1,-2) when A= (x^2y^2z)i + (x^3y^3z^2)j + (xyz^2)k?

the resultant of two vector will be maximum if the are?