Question

If point (-1,0,1) is the origin. Find the $\overrightarrow r$ of point (1,1,0).

Answer 1

We try to use some general concepts of vectors for finding the position vector to solve this question. To find the position vector of a point we subtract final coordinates (that is the origin) from initial coordinates.

Complete step by step answer:
Given the terminal point or the origin is (-1,0,1)
Vector representing the origin is$\overrightarrow t = - 1{i^ \wedge } + 0{j^ \wedge } + 1{k^ \wedge }$
Given the coordinates of the initial point is (1,1,0). Vector representing the initial point is, $\overrightarrow s = 1{i^ \wedge } + 1{j^ \wedge } + 0{k^ \wedge }$

To get the position vector $\left( {\overrightarrow r } \right)$ find the difference of the initial point and the origin.
$\overrightarrow r = \overrightarrow a - \overrightarrow t$
Substituting the values we get,
$\overrightarrow r = \left( {1{i^ \wedge } + 1{j^ \wedge } + 0{k^ \wedge }} \right) - \left( { - 1{i^ \wedge } + 0{j^ \wedge } + 1{k^ \wedge }} \right) \\\ \therefore\overrightarrow r = \left( {2{i^ \wedge } + 1{j^ \wedge } - 1{k^ \wedge }} \right) \\\$
Hence, the position vector of point (1,1,0) is $\overrightarrow r = \left( {2{i^ \wedge } + 1{j^ \wedge } - 1{k^ \wedge }} \right)$.

Additional information:
Position vector is a straight line with one end fixed at the origin and the other end attached to a moving point. It is used to describe the position of the point relative to the origin. As the point moves, there will be a change in length or in direction or in both length and direction.

Note: Sign of the components of the position vector should be kept in mind during calculation to get the right result. It is important to know that the vector $\overrightarrow r$ is known as a position vector or the location vector. To find it we subtract final coordinates from initial coordinates.