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  • Provide solution for RD Sharma maths class 12 chapter 28 The Plane exercise multiple choice question 18

Provide solution for RD Sharma maths class 12 chapter 28 The Plane exercise multiple choice question 18

Answers (1)

Answer:

 Option (a)

Hint:

 Use simultaneous equation.

Given:

 The equation of the plane which cuts equal intercepts of unit length of the co-ordinate axes.

Solution:

We know that the general equation of a planes

Ax+By+Cz+D=0, \text { where } D\neq 0 \qquad \qquad \dots(1)

Here, A, B, C are the coordinate of a normal vector to the plane, while (x, y, z) are the coordinates of any point through which the plane passes.

Again, we know the intercept form of plane

\frac{x}{a}+\frac{y}{b}+\frac{z}{c}=1 \qquad \qquad \dots(2), \text { where }A=\frac{D}{a},B=-\frac{D}{b},C=-\frac{D}{c} A

And the plane makes intercepts at (a, 0, 0), (0, b, 0) and (0, 0, c) with the axes x, y, z respectively.

Here a = b = c = 1

Put in the equation (2)

\frac{x}{1}+\frac{y}{1}+\frac{z}{1}=1

Hence the equation is x + y + z = 1

Posted by

Gurleen Kaur

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