Question

$\overline{a}=x\hat{i}+y\hat{j}+z\hat{k},\overline{b}=\hat{j}$ then the vector $\overline{c}$ for which $\overline{a},\overline{b},\overline{c}$ form a right hand triad

• A. $x(\hat{i}-\hat{k})$
• B. $\overline{0}$
• C. $-z\hat{i}+x\hat{k}$
• D. $y\hat{j}$

Answer 1

The correct option is C $-z\hat{i}+x\hat{k}$

Three vectors a, b and c are said to form a right handed system if a right threaded screw when rotated from a to b the screw moves in direction of c.

Even you can say that axb=c

$\overrightarrow{c}=\left|\begin{array}{ccc}\hat{i}& \hat{j}& \hat{k}\\ x& y& z\\ 0& 1& 0\end{array}\right|$

$\overrightarrow{c}=\hat{i}(-z)-\hat{j}\left(0\right)+\hat{k}\left(x\right)$

$\overrightarrow{c}=-z\hat{i}+x\hat{k}$