Question

The vector with initial point P (2, -3, 5) and terminal point Q (3, -4, 7) is
$$\begin{gathered} \left(\mathrm{a}\right)\hat{i}-\hat{j}+2\hat{k} \\ \left(\mathrm{b}\right)5\hat{i}-7\hat{j}+12\hat{k} \\ \left(\mathrm{c}\right)-\hat{i}+\hat{j}-2\hat{k} \\ \left(\mathrm{d}\right)\mathrm{none}\mathrm{of}\mathrm{these} \end{gathered}$$

Answer 1

Given:
vector with initial point P (2, −3, 5) and terminal point Q (3, −4, 7)

The required vector joining P and Q is the vector $\overrightarrow{PQ}$, given by

$$\begin{gathered} \overrightarrow{PQ}=\left(3-2\right)\hat{i}+\left(-4-\left(-3\right)\right)\hat{j}+\left(7-5\right)\hat{k} \\ \Rightarrow \overrightarrow{PQ}=\hat{i}-\hat{j}+2\hat{k} \end{gathered}$$

Hence, the correct option is (a).