TS EAMCET · Maths · Straight Lines
A vector a has components \(2 p\) and 1 with respect to a two dimensional rectangular cartesian system. This system is rotated through a certain angle about the origin in the counter-clockwise direction. If a has components \(p+\mathrm{l}\) and \(\mathrm{l}\) with respect to the new system, then
- A \(p=1\) or \(p=\frac{-1}{3}\)
- B \(p=-1\) or \(p=\frac{1}{3}\)
- C \(p=1\) or \(p=-1\)
- D \(p=0\) or \(p=\frac{1}{2}\)
Answer & Solution
Correct Answer
(A) \(p=1\) or \(p=\frac{-1}{3}\)
Step-by-step Solution
Detailed explanation
Let point \(A(2 p, 1)\) A is rotated about origin in the anti-clock wise direction then new coordinate is \((p+1,1)\) \(\because \quad 2 p=(p+1) \cos \theta-\sin \theta\) ...(i) and \(1=(p+1) \sin \theta+\cos \theta\) ...(ii) Squaring and adding Eqs. (i) and (ii), we get…
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