Browse Questions

# Find the scalar and vector components of the vector with initial point $(2, 1)$ and terminal point $(– 5, 7).$

$\begin{array}{1 1}(A) \; -7\hat i + 6\hat j\; and \;-7,6 \\ (B) \; -7\hat i - 6\hat j\; and \;7,-6 \\ (C)\; -7\hat i - 6\hat j\; and\; -7,-6 \\ (D)\; 7\hat i + 6\hat j\; and \;7,6 \end{array}$

Toolbox:
• If the initial point is $A(x_1,y_1)$ and the terminal point is $B(x_2,y_2)$,then $\overrightarrow{AB}=(x_2-x_1)\hat i+(y_2-y_1)\hat j$.
Step 1:
Let $A(2,1)$ be the initial point and $B(-5,7)$ be the terminal point.
From the information in the tool box we get
$\overrightarrow{AB}\;\;=(x_2-x_1)\hat{i}+(y_2-y_1)\hat{j}$
$\qquad=(-5-2)\hat{i}+(7-1)\hat{j}$
$\qquad=-7\hat{i}+6\hat{j}$
Step 2:
Hence the vector components are $-7\hat i$ and $6\hat j$ and scalar components are -7 and 6.