AP EAMCET · Maths · Vector Algebra
If the vector \(\overline{\mathrm{i}}-7 \overline{\mathrm{j}}+2 \overline{\mathrm{k}}\) is along the internal bisector of the angle between the vectors \(\bar{a}\) and \(-2 \bar{i}-\bar{j}+2 \bar{k}\) and the unit vector along \(\bar{a}\) is \(x \bar{i}+y \bar{j}+z \bar{k}\) then \(\mathrm{x}=\)
- A 0
- B \(\frac{7}{9}\)
- C \(-\frac{1}{9}\)
- D \(\frac{5}{3}\)
Answer & Solution
Correct Answer
(B) \(\frac{7}{9}\)
Step-by-step Solution
Detailed explanation
\(\left|-2 \bar{i}-\bar{j}+2 \bar{k}\right| = \sqrt{(-2)^2+(-1)^2+(2)^2} = 3\) \(\hat{c} = \frac{-2 \bar{i}-\bar{j}+2 \bar{k}}{3}\) Internal bisector: \(\hat{a} + \hat{c} = \lambda (\overline{\mathrm{i}}-7 \overline{\mathrm{j}}+2 \overline{\mathrm{k}})\)…
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