MTH301 Grand Quiz by Junaid

M

TH301 GRAND QUIZ

Every point in three dimensional space can be described by ------- coordinates

Three

What are the direction cosines for the line joining the points (1, 3, 2) and (7, -2, 3)?

and

The angles which a line makes with positive x ,y and z-axis are known as ------------

Direction angles · Plane parallel to xz-plane · Domain of the function f (x, y, z)=

x y z is

Entire 3D-Space

Suppose f (x, y) = xy− 2y where x2 = +3t 1 and y = 2t. Which one of the following is true?

df t t dt 

For a function f (x, y, z) , the equation ∂∂22xf +∂∂22yf +∂∂22zf =0 is known as

Laplace’s Equation (Ali) · Magnitude of vector a · is 2, magnitude of vectorb is 3 and angle between them when · placed tail to tail is 45 degrees. What is

a b

4.2

Let R be a closed region in two dimensional space. What does the double integral over R calculates?

Two surfaces are said to be orthogonal at a point of their intersection if their normals at that point are ---------

Two surfaces are said to intersect orthogonally if their normals at every point common to them are ----------

Let R be a closed region in two dimensional space. What does the double integral over R calculates?

Two surfaces are said to be orthogonal at a point of their intersection if their normals at that point are ---------

Two surfaces are said to intersect orthogonally if their normals at every point common to them are ---------- and fxy ) in some circle centered at a critical point (x0, y0) and let D = fxx(x0, y0) fyy(x0, y0) − fxy2 (x0, y0) If D > 0 and fxx(x0, y0)

and fxy ) in some circle centered at a critical point (x0, y0) and let D = fxx(x0, y0) fyy(x0, y0) − fxy2(x0, y0) If D = 0 then ---------------