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Vector Joining Two Points

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If `P_1(x_1, y_1, z_1)` and `P_2(x_2, y_2, z_2)` are any two points, then the vector joining `P_1` and `P_2` is the vector  in following fig.

Joining the points `P_1` and `P_2` with the origin O, and applying triangle law, from the triangle `OP_1P_2`, we have
 `vec (OP_1) + vec (P_1P_2) = vec (OP_2)`
Using the properties of vector addition, the above equation becomes
`vec (P_1P_2) = vec (OP_2) - vec (OP_1)`
i.e. `vec (P_1P_2) = (x_2hat i + y_2hatj + z_2hat k) - (x_1hati + y_1hatj + z_1 hat k)`
= `(x_2 - x_1)hat i + (y_2 - y_1)hat j + (z_2 -z_1) hat k`

The magnitude of vector `vec(P_1P_2)` is given by
`|vec (P_1P_2)| = sqrt ((x_2 -x_1)^2  + (y_2 - y_1)^2 + (z_2-z_1)^2)`
 Video link : https://youtu.be/2zP78yNYbMs

Shaalaa.com | Vector Algebra part 12 (Vector joining 2 points)

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Vector Algebra part 12 (Vector joining 2 points) [00:10:47]
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