Vector Algebra Question 384
Question: If the position vectors of the vertices A, B, C of a triangle ABC are $ 7\mathbf{j}+10\mathbf{k}, $ $ -\mathbf{i}+6\mathbf{j}+6\mathbf{k} $ and $ -4\mathbf{i}+9\mathbf{j}+6\mathbf{k} $ respectively, the triangle is
[UPSEAT 2004]
Options:
A) Equilateral
B) Isosceles
C) Scalene
D) Right angled and isosceles also
Show Answer
Answer:
Correct Answer: D
Solution:
- Given, position vectors of $ A,B $ and C are $ 7\mathbf{j}+10\mathbf{k} $ , $ -\mathbf{i}+6\mathbf{j}+6\mathbf{k} $ and $ -4\mathbf{i}+9\mathbf{j}+6\mathbf{k} $ respectively. \ $ |\overrightarrow{AB}|=|-\mathbf{i}-\mathbf{j}-4\mathbf{k}|=\sqrt{18} $ $ |\overrightarrow{BC}|=|-3\mathbf{i}+3\mathbf{j}|=\sqrt{18} $ $ |\overrightarrow{AC}|=|-4\mathbf{i}+2\mathbf{j}-4\mathbf{k}|=\sqrt{36} $ Clearly, $ AB=BC $ and $ {{(AC)}^{2}}={{(AB)}^{2}}+{{(BC)}^{2}} $ Hence, triangle is right angled isosceles.
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