ExamBro
ExamBro
AP EAMCET · Maths · Three Dimensional Geometry

If \(A, B, C\) and \(D\) are points whose position vectors are \(\hat{\mathbf{i}}+\hat{\mathbf{j}}+\hat{\mathbf{k}}, 4 \hat{\mathbf{i}}-\hat{\mathbf{j}}+2 \hat{\mathbf{k}}, 5 \hat{\mathbf{i}}+\hat{\mathbf{j}}\), \(7 \hat{\mathbf{i}}+2 \hat{\mathbf{j}}+3 \hat{\mathbf{k}}\) respectively, then the projection of \(\mathbf{A B}\) on \(\mathbf{C D}\) is

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

Answer & Solution

Correct Answer

(D) \(\sqrt{\frac{7}{2}}\)

Step-by-step Solution

Detailed explanation

Given, position vectors of points \(A, B, C\) and \(D\) are \(\hat{\mathbf{i}}+\hat{\mathbf{j}}+\hat{\mathbf{k}}, 4 \hat{\mathbf{i}}-\hat{\mathbf{j}}+2 \hat{\mathbf{k}}, 5 \hat{\mathbf{i}}+\hat{\mathbf{j}}\) and \(7 \hat{\mathbf{i}}+2 \hat{\mathbf{j}}+3 \hat{\mathbf{k}}\). So,…