Vector Algebra Question 53
Question: If the position vectors of the vertices of a triangle be $2 \hat{i}+4 \hat{j}-\hat{k}, 4 \hat{i}+5 \hat{j}+\hat{k}$ and $3 \hat{i}+6 \hat{j}-3 \hat{k}$, then the triangle is
[UPSEAT 2004]
Options:
A) Right-angled
B) Isosceles
C) Equilateral
D) Right angled isosceles
Show Answer
Answer:
Correct Answer: D
Solution:
- $ \mathbf{a}=2\mathbf{i}+\mathbf{j}+2\mathbf{k}\Rightarrow |a|=\sqrt{4+1+4}=\sqrt{9} $ $ \mathbf{b}=-\mathbf{i}+\mathbf{j}-4\mathbf{k}\Rightarrow |b|=\sqrt{1+1+16}=\sqrt{18} $ $ \mathbf{c}=-\mathbf{i}-2\mathbf{j}+2\mathbf{k}\Rightarrow |c|=\sqrt{1+4+4}=\sqrt{9} $ $ |\mathbf{a}|=|\mathbf{c}| $ and also, $ {{\mathbf{b}}^{2}}={{\mathbf{a}}^{2}}+{{\mathbf{c}}^{2}} $ Hence it is isosceles and right angled triangle.
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