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TS EAMCET · Maths · Vector Algebra

If the position vectors of the vertices of \(\triangle A B C\) are \(3 \hat{\mathbf{i}}+4 \hat{\mathbf{j}}-\hat{\mathbf{k}}, \hat{\mathbf{i}}+3 \hat{\mathbf{j}}+\hat{\mathbf{k}}\) and \(5(\hat{\mathbf{i}}+\hat{\mathbf{j}}+\hat{\mathbf{k}})\), respectively. Then, the magnitude of the altitude from \(A\) onto the side \(B C\) is

  1. A \(\frac{4}{3} \sqrt{5}\)
  2. B \(\frac{5}{3} \sqrt{5}\)
  3. C \(\frac{7}{3} \sqrt{5}\)
  4. D \(\frac{8}{3} \sqrt{5}\)
Verified Solution

Answer & Solution

Correct Answer

(A) \(\frac{4}{3} \sqrt{5}\)

Step-by-step Solution

Detailed explanation

Let altitude of a triangle be \(p\). Now, \(\begin{aligned} & {AB}=-2 \hat{\mathbf{i}}-\hat{\mathbf{j}}+2 \hat{\mathbf{k}} \\ & {AC}=2 \hat{\mathbf{i}}+\hat{\mathbf{j}}+6 \hat{\mathbf{k}} \\ & {BC}=4 \hat{\mathbf{i}}+2 \hat{\mathbf{j}}+4 \hat{\mathbf{k}} \end{aligned}\) We know…