ExamBro
ExamBro
AP EAMCET · Maths · Vector Algebra

Let \(\hat{i}-\hat{j}+2 \hat{k}\) and \(\hat{i}+2 \hat{j}-2 \hat{k}\) be the position vectors of points \(\mathrm{A}\) and \(\mathrm{B}\) respectively. If \(\mathrm{C}\) is a point on the line joining \(\mathrm{A}\) and \(\mathrm{B}\) such that \(\mathrm{BC}=10\), then the position vector of \(\mathrm{C}\) can be

  1. A \(\hat{\mathrm{i}}+8 \hat{\mathrm{j}}-10 \hat{\mathrm{k}}\)
  2. B \(\hat{i}+4 \hat{j}-6 \hat{k}\)
  3. C \(\hat{\mathrm{i}}-8 \hat{\mathrm{j}}+10 \hat{\mathrm{k}}\)
  4. D \(\hat{\mathrm{i}}-4 \hat{\mathrm{j}}-6 \hat{\mathrm{k}}\)
Verified Solution

Answer & Solution

Correct Answer

(A) \(\hat{\mathrm{i}}+8 \hat{\mathrm{j}}-10 \hat{\mathrm{k}}\)

Step-by-step Solution

Detailed explanation

\(\overrightarrow{\mathrm{OA}}=\hat{\mathrm{i}}-\hat{\mathrm{j}}+2 \hat{\mathrm{k}}, \overrightarrow{\mathrm{OB}}=\hat{\mathrm{i}}+2 \hat{\mathrm{j}}-2 \hat{\mathrm{k}}\)…