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TS EAMCET · Maths · Vector Algebra

If \(A(1,1,2), B(4,2,1)\) and \(C(2,3,5)\) are the vertices of a triangle, then a vector representing the median of the triangle through \(A\) is

  1. A \(3 \hat{i}+4 \hat{j}+5 \hat{k}\)
  2. B \((1+2 t) \hat{\mathrm{i}}+\left(1+\frac{3 t}{2}\right) \hat{\mathrm{j}}+(2+t) \hat{\mathrm{k}}\)
  3. C \(2 t \hat{\mathrm{i}}+(7 t-1) \hat{\mathrm{j}}+5 t^2 \hat{\mathrm{k}}\)
  4. D \(7 t^2 \hat{i}+6 \hat{j}+4 \hat{k}\)
Verified Solution

Answer & Solution

Correct Answer

(B) \((1+2 t) \hat{\mathrm{i}}+\left(1+\frac{3 t}{2}\right) \hat{\mathrm{j}}+(2+t) \hat{\mathrm{k}}\)

Step-by-step Solution

Detailed explanation

Since \(A D\) is median \(\therefore \quad D=\left(\frac{4+2}{2}, \frac{2+3}{2}, \frac{1+5}{2}\right)=\left(3, \frac{5}{2}, 3\right)\) \(\therefore\) Equation of \(A D\) is…