Vector Algebra Question 42
Question: Let $ \alpha ,\beta ,\gamma $ be distinct real numbers. The points with position vectors $ \alpha \hat{i}+\beta \hat{j}+\gamma \hat{k},\beta \hat{i}+\gamma \hat{j}+\alpha \hat{k} $ and $ \gamma \hat{i}+\alpha \hat{j}+\beta \hat{k} $
Options:
A) Are collinear
B) Form an equilateral triangle
C) Form a scalene triangle
D) Form a right-angled triangle
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Answer:
Correct Answer: A
Solution:
- [a] $ \alpha ,\beta $ and $ \gamma $ be distinct real numbers $ \alpha \hat{i}+\beta \hat{j}+\gamma \hat{k};\beta \hat{i}+\gamma \hat{j}+\alpha \hat{k};\gamma \hat{i}+\alpha \hat{j}+\beta \hat{k} $ $ \vec{\alpha },\vec{b} $ and $ \vec{c} $ are collinear If $ a=\alpha ,\beta =\beta ,c=\gamma (\because \alpha =\hat{i}+\hat{j}+\hat{k}) $
BETA
