Question

which one of the following is the length of x- intercepts made by the plane 2x – 3y + 4z – 7 = 0 to the co-ordinate axes. *

2

2/7

7/2

7/4​

Answer 1

Step-by-step explanation:

We know, that the general equation of a plane is given by, Ax + By + Cz + D = 0, where D ≠ 0……… (1) Here, A, B, C are the coordinates of a normal vector to the plane, while (x, y, z) are the co - ordinates of any point through which the plane passes. Again, we know the intercept form of plane, which is given by, Where, A = − D a −Da, B = − D b −Db and C = − D c −Dc and the plane makes intercepts at (a, 0, 0), (0, b, 0) and (0, 0, c) with the x - , y - and z - axes respectively. The equation of the plane is given as, 2x–3y + 4z=12 i.e. 2x–3y + 4z - 12=0 ………………… (2) Comparing equation (2) with in the general equation i.e. in equation (1) of plane we get, A=2, B= - 3 and C=4 and D= - 12. The given plane (given by equation (2)) makes intercepts at (6, 0, 0), (0, - 4, 0) and (0, 0, 3)with the x - , y - and z - axes respectively.Read more on Sarthaks.com - https://www.sarthaks.com/1094648/write-the-intercepts-made-by-the-plane-2x-3y-4z-12-on-the-coordinate-axes