For which value of `lambda`, plane `4x + 6y -2z =8` and `2x+3y+ lambda z= 12` are parallel?

For which value of lambda two planes 4x+6y-2z=8 and 2x+3y+ 2 lambda z=12 are parallel?

Find the value of lambda for which the planes 2x-4y+3z=7 and x+2y+lambdaz=18 are perpendicular to each other.

Find the value of lambda , if the line x - 3y + 4 + lambda (8x - 3y + 2) = 0 is parallel to the X-axis .

What is the value of lambda if the straight line (2x + 3y +4) +lambda (6x - y + 12)=0 is parallel to y axis?

Investigate for what values of lambda, mu the simultaneous equations x + y + z = 6, x + 2 y + 3 z = 10 & x + 2 y + lambda z = mu have, An infinite number of solutions.

Investigate for what values of lambda, mu the simultaneous equations x + y + z = 6, x + 2 y + 3 z = 10 & x + 2 y + lambda z = mu have, A unique solution.

The set of all values of lambda for which the systme of linear equations x-2y-2z = lambda x, x +2y +z = lambda y " and "-x-y = lambdaz has a non-trivial solution.

Discuss for all values of lambda , the system of equations x+y+4z =6, x+2y-2z =6, lambda x+ y+z=6 as regards existances and natures of solutions.