Question

Assertion :If position vector is given by $\overrightarrow{r}=sint\hat{i}+cost\hat{j}-7t\hat{k}$, the magnitude of acceleration $\mid \overrightarrow{a}\mid =1$. Reason: The angles which the vector $\overrightarrow{A}=A_1\hat{i}+A_2\hat{j}+A_3\hat{k}$ makes with the coordinate axes are given by $cos\alpha =\frac{A_1}{A},cos\beta =\frac{A_2}{A}$ and $cos\gamma =\frac{A_3}{A}$.

• A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
• B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
• C. Assertion is correct but Reason is incorrect
• D. Assertion is incorrect but Reason is correct

Answer 1

The correct option is B Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion

$\overrightarrow{r}=sint\hat{i}+cost\hat{j}-7t\hat{k}$
$\therefore \overrightarrow{v}=cost\hat{i}-sint\hat{j}+-7\hat{k}$
$\therefore \overrightarrow{a}=-sint\hat{i}-cost\hat{j}$
$\therefore |\overrightarrow{a}|=\sqrt{(-sint{)}^2+(-cost{)}^2}=1$
The ratios of magnitudes of components of the vector to the magnitude of the vector are called directional cosines and given by are given by $cos\alpha =\frac{A_1}{A},cos\beta =\frac{A_2}{A}$ & $cos\gamma =\frac{A_3}{A}$