Practicing Success

Target Exam

CUET

Subject

-- Mathematics - Section B1

Chapter

Vectors

Question:

The value of \(\hat{i}\cdot \left( \hat{j}\times \hat{k}\right)+\hat{j}\left(\hat{i}\times \hat{k}\right)+\hat{k}\cdot \left(\hat{i}\times \hat{j}\right)\) is

Options:

\(0\)

\(-1\)

\(1\)

\(3\)

Correct Answer:

\(1\)

Explanation:
\(\begin{aligned}\hat{i}\cdot (\hat{j}\times \hat{k})+\hat{j}\cdot (\hat{i}\times \hat{k})+\hat{k}\cdot (\hat{i}\times \hat{j})&=\hat{i}\times \hat{i}+\hat{j}\cdot (-\hat{j})+\hat{k}\cdot \hat{k}\\ &=1-1+1\\ &=1\end{aligned}\)