Find the distance between the points `(1,sqrt(3),0) and (1,1/(sqrt(3)),(2sqrt(2))/(sqrt(3)))`.

Prove that the point A (0,0,0),B(2,0,0), C(1,sqrt3,0) and D(1,1/sqrt3, (2sqrt2)/sqrt3) are the vertices of a regular tetrahedron.

Find two irational numbers between sqrt2 and sqrt3

Find the angle between the lines whose direction cosines are (-(sqrt3)/(4), (1)/(4), -(sqrt3)/(2)) and (-(sqrt3)/(4), (1)/(4), (sqrt3)/(2)) .

Find the acute angles between the st. lines : sqrt3 x+y =1 and x+sqrt3 y=1 .

Find angles between the lines sqrt3 x+ y = 1 and x + sqrt3y = 1.

Find the value of the determinant |{:(-1,2,1),(3+2sqrt(2),2+2sqrt(2),1),(3-2sqrt(2),2-2sqrt(2),1):}|

A square of side a lies above the X- axis and has one vertex at the origin . The side passing through the origin makes an angle pi//6 with the positive direction of X-axis .The equation of its diagonal not passing through the origin is y(sqrt(3)-1)-x(1-sqrt(3))=2a y(sqrt(3)+1) +x(1-sqrt(3))=2a y(sqrt(3)+1)+x(1+sqrt(3)) =2a y(sqrt(3)+1)+x(sqrt(3)-1)=2a

Find the value of (sqrt(3)+sqrt(2))^(6)+(sqrt(3)-sqrt(2))^(6)

Find the value of determinant |[sqrt((13))+sqrt(3),2sqrt(5),sqrt(5)],[sqrt((15))+sqrt((26)),5,sqrt((10))],[3+sqrt((65)),sqrt((15)),5]|