Analytic Geometry

b) Find the cylindrical coordinates of the points where the Cartesian coordinates are (2)
i) )8,6,6(
ii) ( 1,1,2 )

Analytic Geometry

Suppose u, v and w are vectors in 3-space,where u =(u1u2, u3), v =(v1, v2, v3) and w= (w1, w2, w3).
Express ( u * v) * w as a determinant.

Analytic Geometry

Find the value of mif it is given that the line y=mxis 4 units from the point (4,-1)
Find the equation of the ciFind the equation of the tangent with the slope 3/4
to the circle x^2+y^2=13
which is tangent to the x at (6,0) and tangent to the y-axis

Analytic Geometry

Show that the closed sphere with centre (2,3,7)and radius 10 in R^3 is contained in the open cube P = {(x, y,z): |x − 2 |<11, |y − 3| <11, |z − 7| <11}.

Analytic Geometry

Show that the closed sphere with centre (2,3,7) 3and radius 10 in 3 R is contained in the
open cube P = {(x, y,z :) x − 2 <11, y − 3 <11, z − 7 <11}.

Analytic Geometry

Which of the following statements are/is true ? Explain why the false one is false

A) If u= (u1,u2) with u(i) not equal to 0 for some 1< i < 2 ( both equal to i ) , then the unit vector in the direction of u is 1/ square root of u(1) squared + u(2) squared * (U(1), u(2)).

B) If u= (1,2,3) find the unit vector in the direction of u.

Analytic Geometry

Which of this is not true?

a.\\(i \times i=j \times j=k \times k=0\\)

b.\\(\alpha \times \beta = \beta \times \alpha \\)

c.\\(\alpha \times \beta =- \beta \times \alpha \\)

d.\\(\alpha \times \beta \neq \beta \times \alpha \\)

Analytic Geometry

Which of this is not true?
a.i*i = j*j = k*k =0
b.α*β = β*α
c.α*β = -β*α
d.α*β = n β*α

Analytic Geometry

b) Find the cylindrical coordinates of the points where the Cartesian coordinates are (2)
i) (6,6,8)
ii) ( SQRT(2),1,1)

Analytic Geometry

a) Express the following surfaces in spherical coordinates
i) xz = 3
ii)x^2+y^2-z^2=1