Find the vector equation of the following planes :
(i) `6x+7y-z=12`
(ii) `x+2 y+3z+5 = 0`

Find the vector equation of the plane x+7y-5z+19=0

Find the vector equation of the following planes whose Cartesian equations are x+2y+3z+5=0

Write the vector equation of the following line: (x-5)/3=(y+4)/7=(6-z)/2

Find the vector equation of the following planes whose Cartesian equations are 2x+3y-z-1=0

Find the values of x and y from the following : (i) (3x -7)+2iy=-5y+(5+ x)i (ii) 2x i+12= 3y-6i (iii) z=x+iy and i(z+2)+1=0 (iv) ((1+i)x-2i)/(3+i)+((2-3i)y+i)/(3-i)=i (v) (3x-2iy)(2+i)^(2)=10(1+i)

Factorize each of the following expressions: (i) 3-12(a-b)^2 (ii) x(x+z)-y(y+z)

Find the vector equation of the line passing through the point (1,-1,2) and perpendicular to the plane 2 x-y+3z-5=0.

Find the vector equation of the line passing through the point (1,-1,2) and perpendicular to the plane 4x-2y-5z-2=0.

Add the following: (i) x – 3y – 2z , 5x + 7y – 8z , 3x – 2y + 5z

Find the equation of the image of the plane x-2y+2z-3=0 in plane x+y+z-1=0.