Convert `r=4tanthetasectheta` into its equivalent Cartesian equation.

Convert rsintheta=rcostheta+4 into its equivalent Cartesian equation.

Convert r=cos e cthetae^(rcostheta) into its equivalent Cartesian equation.

Convert the following polar coordinates to its equivalent Cartesian coordinates. (i) (2,pi) (ii) (sqrt(3),pi//6)

Convert the following polar coordinates to its equivalent Cartesian coordinates. (i) (2,pi/6) (ii) (2,(11pi)/6)

Find the non-parametric form of vector equation, and Cartesian equation vector equation, and Cartesian equation of the plane passing through the point (0, 1,-5) and parallel to the straight lines vecr=(hati=2hatj-4hatk)+s(2hati+3hatj+6hatk) and vecr=(hati=3hatj-4hatk)+t(hati+hatj+hatk)

Given the plane 5x-2y+4z-9=0 i.Find the coordinates of foot of the perpendicular from the origin to the plane. ii. Find the vector equation and the cartesian equation of this perpendicular .

Find the parametric form of vector equation, and Cartesian equations of the plane containing the line vec(r)=(hat(i)-hat(j)+3hat(k))+t(2hat(i)-hat(j)+4hat(k))" and perpendicular to plane "vec(r)*(hat(i)+2hat(j)+hat(k))=8.

Find the vector equation in parametric form and Cartesian equations of the line passo through (-4, 2,-3) and is parallel to the line (-x-2)/(4)=(y+3)/(-2)=(2z-6)/(3)