AP EAMCET · Maths · Vector Algebra
\(O A B C D\) is a pentagon in which the sides \(O A\) and \(C B\) are parallel and the sides \(O D\) and \(A B\) are parallel. Also, it is given that \(\frac{O A}{C B}=2\), \(\frac{O D}{A B}=\frac{1}{3} \cdot\) If \(O A=\mathbf{a}, \mathbf{O D}=\mathbf{d}\), then \(\mathbf{A D}+\mathbf{O C}+\mathbf{D C}=\)
- A \(d-a\)
- B \(\frac{1}{2} a+3 d\)
- C \(\frac{1}{2} a+2 d\)
- D \(6 d\)
Answer & Solution
Correct Answer
(D) \(6 d\)
Step-by-step Solution
Detailed explanation
Given, \(\mathbf{O A}=\mathbf{a}, \mathbf{O D}=\mathbf{d}\) Also, \(\mathbf{O A}=2 \mathrm{CB} \Rightarrow \mathbf{C B}=\frac{\mathbf{O A}}{2}=\frac{\mathbf{a}}{2}\) and \(3 \mathrm{OD}=\mathbf{A B} \Rightarrow \mathbf{A B}=3 \mathbf{d}\) Now,…
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