Question Details

The direction ratios of the normal to the plane 7x + 4y – 2z + 5 = 0 are

Options

A

7, 4,-2

B

7, 4,5

C

7, 4,2

D

4, -2, 5

Correct Answer :

7, 4,-2

Solution :

The correct option is 7, 4, -2.

To understand why this is the correct answer, let us look at the general equation of a plane in three-dimensional space.
The general equation of a plane is represented as:

ax+by+cz+d=0

where a, b, and c are the coefficients of x, y, and z respectively, and d is a constant term.

In this general form, the coefficients (a,b,c) directly represent the direction ratios of the normal vector (a vector perpendicular) to the plane.

Now, let us compare the given equation of the plane with the general equation:
Given equation:

7x+4y2z+5=0

By comparing the coefficients, we get:
a=7
b=4
c=2

Therefore, the direction ratios of the normal to the plane are (a,b,c), which are equal to 7, 4, -2.

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