Question

Seven people wearing shirts with the slogan of ‘Reduce air pollution through
plantations’ are standing on a bench represented by X-axis. The spot light is placed at
the point (7, 3 , 4). What is the distance of spotlight from the bench?

Answer 1

Answer:

The distance between the point where the spot light is kept at (7, 3, 4) and the bench kept at X-axis is 8.6 units.

Step-by-step explanation:

The distance between 2 points 'd' in 3D, points P1 (x1, y1, z1) and point P2 (x2, y2, z2) is given by

d= √((x2-x1)²+(y2-y1)²+(z2-z1)²)

Answer 2

Answer:

As, here we have to find The distance between a point on the bench which is  on X axis in three dimensional plane.

When we talk about three dimensional plane , we include Z coordinate in the system of two dimensional coordinate system.

Any point in three dimensional plane is represented as (x,y,z)

Here point on the bench is on x axis, so other two coordinates will be zero.

So, point on x axis is represented as (x,0,0).

Another point , which is spotlight has coordinates =(7,3,4)

Formula for distance between two points , (a,b,c) and (p,q,r) is given as:

   $=\sqrt{(a-p)^2+(b-q)^2+(c-r)^2$

So, distance between point on the bench (x,0,0) and spotlight (7,3,4)

$=\sqrt{(7-x)^2+(3-0)^2+(4-0)^2}\\\\=\sqrt{(7-x)^2+9+16}\\\\=\sqrt{(7-x)^2+25}$