Question

find vector A from origin to a point in between R1 and R2 at a distance xr from the point R1



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Answer 1

Consider two points located at vector r_1 and vector r_2, separated by distance r_12 = r_1 - r_2. Find a vector A from the origin to the point on the line between r_1 and r_2 at a distance x from the point at r_1 where x is some number. Express your answer in terms of r_1, r_2, r_12, and x.

Answer 2

Answer:

The vector A from origin to a point in between R1 and R2 is A = xr(R2 - R1)/|R2 - R1|

Explanation:

From the above question,

They have given :

Consider points located at a separated distance vector from the origin between the distance of the point 1 and point 2 is 4 units.

The equation for this vector is given by:

r1 = (x1, y1, z1) and r2 = (x2, y2, z2)

where x1, y1 and z1 are the coordinates of point 1 and x2, y2, and z2 are the coordinates of point 2.

The distance between point 1 and point 2 is given by:

d = sqrt((x2-x1)^2 + (y2-y1)^2 + (z2-z1)^2)

In this case, the distance between point 1 and point 2 is 4 units, so we can solve for the coordinates of each point:

x1 = 0, y1 = 0, z1 = 0

x2 = sqrt(4^2 - 0^2 - 0^2) = 4

y2 = 0

z2 = 0

Therefore, the coordinates of each point are:

Point 1: (0, 0, 0)

Point 2: (4, 0, 0)

Hence,

    The vector A from origin to a point in between R1 and R2 is A = xr(R2 - R1)/|R2 - R1|

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