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TS EAMCET · Maths · Three Dimensional Geometry

Assertion (A) The direction ratios of line \(L_1\) are 2, 5, 7 and those of line \(L_2\) are \(\frac{4}{\sqrt{19}}, \frac{10}{\sqrt{19}}\), \(\frac{14}{\sqrt{19}}\). The lines \(L_1, L_2\) are parallel.Reason (R) The direction ratios of a line \(L_1\) are \(a_1, b_1, c_1\) and those of another line \(L_2\) are \(a_2, b_2, c_2\). The lines \(L_1\) and \(L_2\) are parallel if \(a_1 a_2+b_1 b_2+c_1 c_2=0\) The correct option among the following is

  1. A (A) is true, \((R)\) is true and \((R)\) is the correct explanation for \((A)\).
  2. B (A) is true, \((R)\) is true but \((R)\) is not the correct explanation for \((A)\).
  3. C \((A)\) is true but \((R)\) is false.
  4. D (A) is false but \((R)\) is true.
Verified Solution

Answer & Solution

Correct Answer

(C) \((A)\) is true but \((R)\) is false.

Step-by-step Solution

Detailed explanation

Let the direction ratios of a line \(L_1\) be \(a_1, b_1, c_1\) and those of another line \(L_2\) are \(a_2, b_2, c_2\) and the angle \(\theta\) between them is given by \(\cos \theta=\frac{a_1 a_2+b_1 b_2+c_1 c_2}{\sqrt{a_1^2+b_1^2+c_1^2} \sqrt{a_2^2+b_2^2+c_2^2}}\)…