Question

# If Vector $\overrightarrow {AB} = 2\hat i - \hat j + \hat k$ & $\overrightarrow {OB} = 3\hat i - 4\hat j + 4\hat k$, finds the position vector $\overrightarrow {OA}$.

Hint: A quantity having magnitude as well as direction is known as vector, necessary for finding the position of one point in space with respect to others. Vectors are represented by a line symbol $\to$on the top of the variable that determines the magnitude and direction of the quantity.
In this question we have to find the position vector of $\overrightarrow {OA}$ by using the triangle law of addition of the vector.
$\overrightarrow {AB} = 2\hat i - \hat j + \hat k$
$\overrightarrow {OB} = 3\hat i - 4\hat j + 4\hat k$
The position vector of $\overrightarrow {OA}$the straight line point where $O$is a fixed point and $A$is the moving point, here the vectors make a triangle hence we will use triangle law of vector addition which states when the two sides of triangle represent magnitude and direction then its third side will represent the magnitude and direction of their sum hence we can write $\overrightarrow {OA} = \overrightarrow {AB} + \overrightarrow {OB}$, so the position vector of $\overrightarrow {OA}$ is equal to
$\overrightarrow {OA} = \overrightarrow {AB} + \overrightarrow {OB} \\ = 2\hat i - \hat j + \hat k + 3\hat i - 4\hat j + 4\hat k \\ = \left( {2 + 3} \right)\hat i + \left( { - 1 - 4} \right)\hat j + \left( {1 + 4} \right)\hat k \\ = 5\hat i - 5\hat j + 5\hat k \\$
Hence the position vector of $\overrightarrow {OA}$ $= 5\hat i - 5\hat j + 5\hat k$