Q17 of 230 Page 29

Find the equation of the plane passing through (a, b, c) and parallel to the plane ?

Given that equation is parallel to so that


The normal vector to that plane will be …… (1)


And equation of the plane passing through the point is


a1(x – x1) + b1(y – y1) + c1(z – z1) = 0


and point is (a, b, c) so that,


a1(x – a) + b1(y – b) + c1(z – c) = 0


by equation (1) a1 = b1 = c1 = 1


x + y + z – a – b – c = 0


x + y + z = a + b + c


More from this chapter

All 230 →
15

Find the equation of family of planes through the line of intersection of the planes 3x – y + 2z = 4 and x + y + z = 2 which is passing through (2, 2, 1)?

 16

Find the equation of family of planes through the line of intersection of the planes x + y + z = 1 and 2x + 3y + 4z = 5 which is perpendicular to the plane x – y + z = 0 and parallel to ?

 18

Find the equation of the plane which contains the line of intersection of the plane x + 2y + 3z – 4 = 0 and 2x + y – z + 5 = 0 and whose x – intercept is twice of z – intercept. Hence, write the equation of the plane passing through the point (2,3, – 1) and parallel to the plane obtained above?

 19

Find the equation of the plane through the line of intersection of the plane x + y + z = 1 and 2x + 3y + 4z = 5 and twice of its y–intercept is equals to the three times its z intercept?