Vector Algebra Question 381
Question: The distance between the planes given by $ \mathbf{r}.(\mathbf{i}+2\mathbf{j}-2\mathbf{k})+5=0 $ and $ \mathbf{r}.(\mathbf{i}+2\mathbf{j}-2\mathbf{k})-8=0 $ is
Options:
A) 1 unit
B) $ \frac{13}{3} $ unit
C) 13 unit
D) None of these
Show Answer
Answer:
Correct Answer: B
Solution:
- The two planes are on the opposite side of the origin. Therefore, if $ p_1 $ and $ p_2 $ are the lengths of the perpendicular from the origin to the planes $ \mathbf{r}.(\mathbf{i}+2\mathbf{j}-2\mathbf{k})+5=0 $ and $ \mathbf{r}.(\mathbf{i}+2\mathbf{j}-2\mathbf{k})-8=0 $ respectively, then the required distance is given by $ p_1+p_2=\frac{5}{3}+\frac{8}{3}=\frac{13}{3} $ unit.
BETA
