Vectors Question 192
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} $ do not form
Options:
A) an equilateral triangle
B) isosceles triangle
C) a right angled triangle
D) no triangle
Correct Answer: A [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, triangle ABC will be a right-angled triangle.
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Solution:
BETA
