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Vector Calculus
evaluate ∇ × r(vector) / r(magnitude)
Vector Calculus
Find the direction in which the function f= x^2-y^2+2xy decreases more rapidly at the point (1,1)
Vector Calculus
Explain why it is not possible for two of a vector's direction angles to be less than 45°
Vector Calculus
if the force field defined by vector F=(3x^2yz-3y)i^ + (x^3z - 3x)j^ + (x^3y+2z)k^ conservative? if so, find the scalar potenial associated with the vector F.
Vector Calculus
A plane sheet of material is bound by the curve y = x^2 from x = 0 to x = 1 the x-axis
and the line x = 1. If the mass per unit area (density) of the sheet is xy find the mass of
the sheet
and the line x = 1. If the mass per unit area (density) of the sheet is xy find the mass of
the sheet
Vector Calculus
Show that
(vr .∇) vr = 1/2(∇v^2)− vr × (∇×vr)
Note: here vr= vector r
(vr .∇) vr = 1/2(∇v^2)− vr × (∇×vr)
Note: here vr= vector r
Vector Calculus
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 .
f ( X, Y, Z) =X^2YZ^3 + 20 .
Vector Calculus
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
with its centre at the origin and radius of 4 units.
note ^i=icap(unit vector) so on for other
Vector Calculus
A boat sails 3 km South, then 10 km Southeast. Use trigonometry to find the boat's distance and bearing from its starting point.
Vector Calculus
Research an example of the use of vectors, and explain how the mathematics is used, for example in engineering, computer animation, gaming, 3-D printing or GPS technology.
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