Kinematics Question 426
Question: The three vectors $ \vec{A}=3\hat{i}-2\hat{j}-\hat{k}, $ $ \vec{B}=\hat{i}-3\hat{j}+5\hat{k} $ and $ \vec{C}=2\hat{i}-\hat{j}-4\hat{k} $ does not form
Options:
A) an equilateral triangle
B) isosceles triangle
C) a right angled triangle
D) no triangle
Show Answer
Answer:
Correct Answer: A
Solution:
[a]
$ \vec{A}=3\hat{i}-2\hat{j}+\hat{k},\vec{B}=\hat{i}-3\hat{j}+5\hat{k},\vec{C}=2\hat{i}-\hat{j}+4\hat{k} $
$ |\vec{A}|=\sqrt{3^{2}+{{(-2)}^{2}}+1^{2}}=\sqrt{9+4+1}=\sqrt{14} $
$ |\vec{B}|=\sqrt{1^{2}+{{(-3)}^{2}}+5^{2}}=\sqrt{1+9+25}=\sqrt{35} $
$ |\vec{C}|=\sqrt{2^{2}+1^{2}+{{(-4)}^{2}}}=\sqrt{4+1+16}=\sqrt{21} $ As $ B=\sqrt{A^{2}+C^{2}} $
therefore ABC will be right angled triangle.
BETA
