Question

Statement $1:$ Scalar components of the vector with initial point $(2,1)$ and terminal point $(-5,7)$ are $-6$ and $-7.$
Statement $2:$ Vector components of the vector with initial point $(2,1)$ and terminal point $(-5,7)$ are $-7\hat{i}$ and $6\hat{j}$.

• A. Only statement $1$ is correct
• B. Only statement $2$ is correct
• C. both statements are true
• D. both statements are false

Answer 1

The correct option is B Only statement $2$ is correct

A vector with initial point $(x_1,y_1)$ and terminal/final point $(x_2,y_2)$ is given $(x_2-x_1)\hat{i}+(y_2-y_1)\hat{j}$
$\Rightarrow$vector with initial point $A(2,1)$ and final point $B(-5,7)$ can be given by
$\overrightarrow{AB}=(x_2-x_1)\hat{i}+(y_2-y_1)\hat{j}=(-5-2)\hat{i}+(7-1)\hat{j}$
$=(-7)\hat{i}+6\hat{j}$
Hence, the required scalar components (coefficients of $\hat{i}$ and $\hat{j}$) are $-7$ and $6$ while the vector components are $-7\hat{i}$ and $6\hat{j}$