ExamBro
ExamBro
TS EAMCET · Maths · Vector Algebra

If the position vectors of \(P\) and \(Q\) are \(\hat{i}+2 \hat{j}-7 \hat{k}\) and \(5 \hat{i}-3 \hat{j}+4 \hat{k}\) respectively, then the cosine of the angle between \(\overrightarrow{\mathrm{PQ}}\) and \(\mathrm{z}\)-axis is

  1. A \(\frac{4}{\sqrt{162}}\)
  2. B \(\frac{11}{\sqrt{162}}\)
  3. C \(\frac{5}{\sqrt{162}}\)
  4. D \(\frac{-5}{\sqrt{162}}\)
Verified Solution

Answer & Solution

Correct Answer

(B) \(\frac{11}{\sqrt{162}}\)

Step-by-step Solution

Detailed explanation

\(\overrightarrow{P Q}=(5 \hat{i}-3 \hat{j}+4 \hat{k})-(\hat{i}+2 \hat{j}-7 \hat{k})\) \(\overrightarrow{P Q}=4 \hat{i}-5 \hat{j}+11 \hat{k}\) Equation of \(z\)-axis : \(\hat{k}\)…