First slide

Direction ratios and direction cosines

Question

If $\bar{r}$ is a vector of magnitude 210 and has direction ratios $2, - 3, 6$ , then $\bar{r}$ =

Easy

A

$60 \bar{i} - 90 \bar{j} + 180 \bar{k}$
B

$120 \bar{i} - 180 \bar{j} - 36 \bar{0 k}$
C

$12 \bar{i} + 18 \bar{j} - 36 \bar{k}$
D

$7 (12 \bar{i} + 18 \bar{j} + 36 \bar{k})$

Solution

The vector along another vector $\bar{a}$ with magnitude $k$ units is $k (\frac{\bar{a}}{|\bar{a}|})$
Hence, the vector $\bar{r}$ with magnitude 210 units along the vector $2 i - 3 j + 6 k$ is $210 (\frac{2 i - 3 j + 6 k}{\sqrt{4 + 9 + 36}})$
Therefore, $\bar{r} = 60 i - 90 j + 180 k$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App