If the new coordinates of the point (1,2,3) when the origin shifts from (0,0,0) to (3,4,6) is (l,m,n) then find the value of -(l+m+n)
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If the new coordinates of the point (1,2,3) when the origin shifts from (0,0,0) to (3,4,6) is (l,m,n) then find the value of -(l+m+n)
How coordinates change when we shift origin from (0,0,0) to another point is similar to the one we saw in the case of shifting origin in two dimensional geometry. If the origin moves from (0,0,0) to (a,b,c) then the new coordinates of the point (x,y,z) will be (x-a, y-b, z-c).
(An intuition behind this is , when we are finding the coordinates of a point, we are seeing how many units we have to move along the axes to reach the point. Now that the origin is (a,b,c), we will have to move x-a units in the direction of x -axis. Similarly, y and z coordinates)
In our question, origin moves from (0,0,0) to (3,4,6) and we want to find the new coordinates of (1,2,3).
It would be (1-3, 2-4, 3-6) = (-2, -2, -3)
This is given as (l, m, n)
⇒-(l+m+n) = - ( -2-2-3)
=7
How coordinates change when we shift origin from (0,0,0) to another point is similar to the one we saw in the case of shifting origin in two dimensional geometry. If the origin moves from (0,0,0) to (a,b,c) then the new coordinates of the point (x,y,z) will be (x-a, y-b, z-c).
(An intuition behind this is , when we are finding the coordinates of a point, we are seeing how many units we have to move along the axes to reach the point. Now that the origin is (a,b,c), we will have to move x-a units in the direction of x -axis. Similarly, y and z coordinates)
In our question, origin moves from (0,0,0) to (3,4,6) and we want to find the new coordinates of (1,2,3).
It would be (1-3, 2-4, 3-6) = (-2, -2, -3)
This is given as (l, m, n)
⇒-(l+m+n) = - ( -2-2-3)
=7
