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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}.
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
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)
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
i) xz = 3
ii)x^2+y^2-z^2=1
Analytic Geometry
Express the following surfaces in spherical coordinates
i) xz = 3
ii) x^2+y^2-z^2=1
i) xz = 3
ii) x^2+y^2-z^2=1
Analytic Geometry
For vectors U, V, W, show that U.V = V.U and (U + V).W = (U.W) + (V.W)
Analytic Geometry
Find the unit U(A) of a vector A = -20I + 36J. Given a vector A, U(A) is defined as A/|A|
