Which of the following is parallel to plane 3x - 3y +4z = 7?
Which of the following is parallel to plane 3x - 3y +4z = 7?
The correct option is A 3x - 3y +4z = 1
We know that the equation of a plane parallel to ax +by + cz + d = 0 can be given by
ax +by + cz + k = 0 , since the normal vector to both the plane will be same.
So, the equation of a plane parallel to 3x - 3y +4z = 7 will be 3x - 3y +4z = k where k can be any real constant. Out of the options given we have 3x - 3y +4z = 1 as the correct answer.
Note - As in the equation of plane ax +by + cz + d, a,b,c are the direction ratios of normal. The equation of a plane parallel to it can be 2ax+ 2by+ 2cz + k = 0 because here the direction ratios of normal 2a,2b, 2c will lead to same direction cosines of that vector. So in the equation of a plane parallel to another plane the coefficients of x,y,z should be in such a way that they can be formed by multiplying the direction ratios of the given plane with a constant number.
3x - 3y +4z = 1
We know that the equation of a plane parallel to ax +by + cz + d = 0 can be given by
ax +by + cz + k = 0 , since the normal vector to both the plane will be same.
So, the equation of a plane parallel to 3x - 3y +4z = 7 will be 3x - 3y +4z = k where k can be any real constant. Out of the options given we have 3x - 3y +4z = 1 as the correct answer.
Note - As in the equation of plane ax +by + cz + d, a,b,c are the direction ratios of normal. The equation of a plane parallel to it can be 2ax+ 2by+ 2cz + k = 0 because here the direction ratios of normal 2a,2b, 2c will lead to same direction cosines of that vector. So in the equation of a plane parallel to another plane the coefficients of x,y,z should be in such a way that they can be formed by multiplying the direction ratios of the given plane with a constant number.
