AP EAMCET · Maths · Three Dimensional Geometry
A line segment PQ has the length 63 and direction ratios \((3,-2,6)\). If this line makes an obtuse angle with X -axis, then the components of the vector \(\overline{\mathrm{PQ}}\) are
- A \(7,8,-4\)
- B \(-7,8,-4\)
- C \(27,-18,54\)
- D \(-27,18,-54\)
Answer & Solution
Correct Answer
(D) \(-27,18,-54\)
Step-by-step Solution
Detailed explanation
\(\text{Magnitude of direction ratios } = \sqrt{3^2 + (-2)^2 + 6^2} = \sqrt{9+4+36} = \sqrt{49} = 7\) \(\text{Scaling factor } k = \frac{\text{Length}}{\text{Magnitude of direction ratios}} = \frac{63}{7} = 9\)…
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