ExamBro
ExamBro
TS EAMCET · Maths · Vector Algebra

A vector of magnitude \(\sqrt{2}\) units along the internal bisector of the angle between the vectors \(2 \hat{i}-2 \hat{j}+\hat{k}\) and \(\hat{i}+2 \hat{j}+2 \hat{k}\) is

  1. A \(\hat{j}+\hat{k}\)
  2. B \(\hat{i}-\hat{j}\)
  3. C \(\hat{i}-\hat{k}\)
  4. D \(\hat{i}+\hat{k}\)
Verified Solution

Answer & Solution

Correct Answer

(D) \(\hat{i}+\hat{k}\)

Step-by-step Solution

Detailed explanation

\(\vec{a}=2 \hat{i}-2 \hat{j}+\hat{k}, \vec{b}=\hat{i}+2 \hat{j}+2 \hat{k}\) \(|\vec{a}|=3=|\vec{b}|\) Internal angle bisector is \(\frac{\vec{a}+\vec{b}}{2}=3 \hat{i}+3 \hat{k}\) Vector of magnitude \(\sqrt{2}\) is \(\hat{i}+\hat{k}\).