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TS EAMCET · Maths · Vector Algebra

\(\vec{a}=2 \hat{i}-\hat{j}, \vec{b}=2 \hat{j}-\hat{k}, \vec{c}=2 \hat{k}-\hat{i}\) are three vectors and \(\vec{d}\) is a unit vector perpendicular to \(\vec{c}\). If \(\vec{a}, \vec{b}, \vec{d}\) are coplanar vectors, then \(|\vec{d} \cdot \vec{b}|=\)

  1. A 0
  2. B \(\frac{1}{\sqrt{14}}\)
  3. C \(\sqrt{\frac{2}{7}}\)
  4. D \(\sqrt{\frac{7}{2}}\)
Verified Solution

Answer & Solution

Correct Answer

(D) \(\sqrt{\frac{7}{2}}\)

Step-by-step Solution

Detailed explanation

\(\vec{a}=2 \hat{i}-\hat{j}, \vec{b}=2 \hat{j}-\hat{k}, \vec{c}=-\hat{i}+2 \hat{k}\) Let \(\vec{d}=\frac{p \hat{i}+q \hat{j}+r \hat{k}}{\sqrt{p^2+q^2+r^2}}\), let \(\vec{d}\) is \(\perp^{\mathrm{r}}\) to \(\bar{c}\)…