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

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.




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 \\)


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
b) Find the cylindrical coordinates of the points where the Cartesian coordinates are (2) i) (6,6,8) ii) ( SQRT(2),1,1)
a) Express the following surfaces in spherical coordinates i) xz = 3 ii)x^2+y^2-z^2=1
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