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AP EAMCET · Maths · Vector Algebra

A unit vector perpendicular to the vectors \(\vec{a}=2 \hat{i}+3 \hat{j}+4 \hat{k}\) and \(\vec{b}=3 \vec{j}+2 \vec{k}\) is

  1. A \(\frac{3 \hat{i}+2 \hat{j}-2 \hat{k}}{\sqrt{22}}\)
  2. B \(\frac{3 \hat{i}+2 \hat{j}-3 \hat{k}}{\sqrt{22}}\)
  3. C \(\frac{3 \hat{i}-2 \hat{j}+3 \hat{k}}{\sqrt{22}}\)
  4. D \(\frac{3 \hat{i}+2 \hat{j}+3 \hat{k}}{\sqrt{22}}\)
Verified Solution

Answer & Solution

Correct Answer

(B) \(\frac{3 \hat{i}+2 \hat{j}-3 \hat{k}}{\sqrt{22}}\)

Step-by-step Solution

Detailed explanation

\(\vec{a} \times \vec{b}=\left|\begin{array}{ccc}\hat{i} & \hat{j} & \hat{k} \\ 2 & 3 & 4 \\ 0 & 3 & 2\end{array}\right|=-6 \hat{i}-4 \hat{j}+6 \hat{k}\) \(\therefore\) Unit vector perpendicular to \(\vec{a}\) and \(\vec{b}\)…