Vector Algebra Question 283
Question: The position vectors of points A and B are $ \mathbf{i}-\mathbf{j}+3\mathbf{k} $ and $ 3\mathbf{i}+3\mathbf{j}+3\mathbf{k} $ respectively. The equation of a plane is $ \mathbf{r}.(5\mathbf{i}+2\mathbf{j}-7\mathbf{k})+9=0 $ . The points A and B
Options:
A) Lie on the plane
B) Are on the same side of the plane
C) Are on the opposite side of the plane
D) None of these
Show Answer
Answer:
Correct Answer: C
Solution:
- The position vectors of two given points are $ \mathbf{a}=\mathbf{i}-\mathbf{j}+3\mathbf{k} $ and $ \mathbf{b}=3\mathbf{i}+3\mathbf{j}+3\mathbf{k} $ the equation of the given plane is $ \mathbf{r}.(5\mathbf{i}+2\mathbf{j}-7\mathbf{k})+9=0 $ or $ \mathbf{r}.,\mathbf{n}+d=0 $ . We have, $ \mathbf{a}.,\mathbf{n}+d=(\mathbf{i}-\mathbf{j}+3\mathbf{k}).(5\mathbf{i}+2\mathbf{j}-7\mathbf{k})+9 $ $ =5-2-21+9<0 $ and, $ \mathbf{b}.\mathbf{n}+d=(3\mathbf{i}+3\mathbf{j}+3\mathbf{k}).(5\mathbf{i}+2\mathbf{j}-7\mathbf{k})+9 $ $ =15+6-21+9>0 $ So, the points a and $ \mathbf{b} $ are on the opposite sides of the plane.
BETA
