Find the vector equation of the line whose Cartesian equation is given by x+y+z=0.

Find the vector equation of the plane whose cartesian from of equation is 3x-4y+2z=5

Find the vector equation of the line passing through the point (2,-1,-1) which is parallel to the line 6x-2=3y+1=2z-2.

The line x/a-y/b=1 cuts the x-axis at P. Find the equation of the line through p and perpendicular to the given line.

Find the lines whose combined equation is 6x^2+5x y-4y^2+7x+13 y-3=0

Find the equation of component lines whose combined equation is 6x^(2)+5xy-4y^(2)+7x+13y-3=0 without solving for xor y.

Find the equation of the ellipse whose foci (0,+-4) and the equation of directries is y=+-9 .

Find Cartesian and vector equation of the line which passes through the point (-2,4,-5) and parallel to the line given by (x+3)/3=(y-4)/5=(z+8)/6 .

(i) Find the vector equation of a line passing through a point with position vector 2hat(i)-hat(j)+hat(k) , and parallel to the line joining the points -hat(i)+4hat(j)+hat(k) and hat(i)+2hat(j)+2hat(k) . Also find the cartesian equivalent of this equation. (ii) The cartesian equations of a line are 6x-2=3y+1=2z-2 . Find its direction ratios and also find vector equation of the line.

Find the cartesian equation of the line which is perpendicular to lines (x)/(2)=(y)/(1)=(z)/(3) and (x-3)/(-1)=(y-2)/(3)=(z+5)/(5) and which passes through the points (1,2,3) and hence convert it to vector form.

Find the equation of the parabola whose vertex is (0,0) and directrix is the line x + 3 = 0 .