Vector Algebra Question 78
Question: The distance between the line $ \mathbf{r}=2\mathbf{i}-2\mathbf{j}+3\mathbf{k}+\lambda (\mathbf{i}-\mathbf{j}+4\mathbf{k}) $ and the plane $ \mathbf{r}.(\mathbf{i}+5\mathbf{j}+\mathbf{k})=5 $ is
[AIEEE 2005]
Options:
A) $ \frac{3}{10} $
B) $ \frac{10}{3} $
C) $ \frac{10}{9} $
D) $ \frac{10}{3\sqrt{3}} $
Show Answer
Answer:
Correct Answer: D
Solution:
- Required distance $ =. | \frac{d-\mathbf{a}.\mathbf{n}}{|\mathbf{n}|} . |=. | \frac{5-(2\mathbf{i}-2\mathbf{j}+3\mathbf{k}).(\mathbf{i}+5\mathbf{j}+\mathbf{k})}{\sqrt{1+25+1}} . | $ $ . =| \frac{5-(2-10+3)}{\sqrt{27}} . | $ $ =\frac{10}{3\sqrt{3}} $ .
BETA
