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TS EAMCET · Maths · Vector Algebra

The points whose position vectors are \(2 \mathbf{i}+3 \mathbf{j}+4 \mathbf{k}, 3 \mathbf{i}+4 \mathbf{j}+2 \mathbf{k}\) and \(4 \mathbf{i}+2 \mathbf{j}+3 \mathbf{k}\) are the vertices of

  1. A an isosceles triangle
  2. B right angled triangle
  3. C equilateral triangle
  4. D right angled isosceles triangle
Verified Solution

Answer & Solution

Correct Answer

(C) equilateral triangle

Step-by-step Solution

Detailed explanation

\begin{aligned} & \text {Let } \mathbf{a}=2 \mathbf{i}+3 \mathbf{j}+4 \mathbf{k}=\mathrm{OA} \\ & \mathbf{b}=3 \mathbf{i}+4 \mathbf{j}+2 \mathbf{k}=\mathrm{OB} \\ & \text {and } \mathbf{c}=4 \mathbf{i}+2 \mathbf{j}+3 \mathbf{k}=\mathrm{OC} \\ & A B=O B-O A=i+j-2 k \\ & B C=O C-O…