Vector Algebra Question 18
Question: The equation $|\vec{r}|^2-\vec{r} \cdot(2 \hat{i}+4 \hat{j}-2 \hat{k})-10=0$ represents a
Options:
A) Circle
B) Plane
C) Sphere of radius 4
D) Sphere of radius 3
Show Answer
Answer:
Correct Answer: C
Solution:
- Since the equation $ |\mathbf{r}{{|}^{2}}-2(\mathbf{r}.\mathbf{a})+\lambda =0 $ represents a sphere of radius $ \sqrt{|\mathbf{a}{{|}^{2}}-\lambda } $ , therefore $ |\mathbf{r}{{|}^{2}}-\mathbf{r}.(2\mathbf{i}+4\mathbf{j}-2\mathbf{k})-10=0 $ represents a sphere of radius $ =\sqrt{|\mathbf{i}+2\mathbf{j}-\mathbf{k}{{|}^{2}}+10}=\sqrt{6+10}=4 $ .
BETA
